Write the correct answer
0 of 24 Questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 24 Questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score 

Your score 

For the A.P. 3, – 7, – 11, … can we find directly \(t_{ 30} – t_{20}\) without actually finding \(t_{30}\) and \(t_{20}\)? Give reasons for your answer.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
It is because difference between any two terms of an AP is proportional to common difference of that AP.
The 4th term of an A.P. is three times the first term and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
…(1)
…(2)
Shonal deposited Rs 1000 at compound interest at the rate of 10% p.a. The amounts at the end of first year, second year, third year …. form an A.P. Justify your answer.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Amount at the end of 1st year = 1000
Amount at the end of 2nd year = 1210
Amount at the end of 3rd year = 1331
As , it does form an AP
Write the expression \(t_n – t_m\) for the A.P. \(a, a + d, a + 2d,\) ….. Hence, find the common difference of the A.P. for which 11th term is 5 and 13th term is 79.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Justify whether it is true to say that 2n – 3 is the nth term of an A.P.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Hence is the nth term of an AP.
If the numbers of x – 2, 4x – 1, and 5x + 2 are in A.P find the value of x
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Verify that each of the following is an A.P. :
(a) x + y, (x + 1) + y, (x + 1) + (y + 1), …
(b) x, 2x + 1, 3x + 2, 4x + 3, …
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(a)
which is the middle term
So it is an AP.
(b)
which is a middle term. So it is an AP.
Find a, b and c, if the numbers a, 7, b, 23, c are in A.P..
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
…(1)
The sum of \(n \) terms of a sequence is \(3n^2 + 4n\). Find the nth term and show that it is an A.P..
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Since constant. The sequence is an AP.
The sum of first \(n \) terms of an A.P. is given by \(3n^2 – n\). Determine the A.P. and its 25th term.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Required AP is 2, 8, 14
so the 25th term of an AP is 146
How many terms of the A.P. \(6\dfrac{11}{2},5 \)…. Are needed to give the sum 25 ?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
\(\)6,\dfrac{11}{2},5\\ \\ S_n=25,\ d=\dfrac{11}{2}+6=\dfrac{11+12}{2}=\dfrac{1}{2}\\ \\ S_n=\dfrac{n}{2}[2a+(n1)d]\\ \\ 25=\dfrac{n}{2}[2a+(n1)d]\\ \\ 25=\dfrac{n}{2}[12+(n1)\times\dfrac{1}{2}]\\ \\ \Rightarrow 50=n[12+\dfrac{n1}{2}]=n\bigg[\dfrac{24+n1}{2}\bigg]\\ \\ \Rightarrow 100=24n+n^2n=25n+n^2\\ \\ \Rightarrow n^225n+100=0\Rightarrow n^220n5n+100=0\\ \\ \Rightarrow n(n20)5(n20)=0\\ \\ \Rightarrow n=5,20\\ \\ S_5=\dfrac{5}{2}[112+2]=\dfrac{5}{2}\times10=25\\ \\ S_{20}=\dfrac{20}{2}\bigg[12+\dfrac{19}{2}\bigg]=10\times\bigg[\dfrac{5}{2}=25 /latex]
If \(t_n=34_n \), show that \(t_1,t_2,t_3,…. \) form an A.P. Also, find \(S_{20} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
So form an AP
Calculate how many multiples of 7 are there between 100 and 300.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let 294 be the nth term of an AP
If \(S_n \) denotes the sum of n terms of an AP whose common difference is d and first term is a, find \(S_n2S_{n1}+S_{n2} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find the sum of first 10 terms of the sequence \(\{a_n\} \) where \(a_n=56n \), where \( n\) is a natural number
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The 8th term of an A.P. is 37 and its 12th term is 57. Find the A.P.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
on subtracting,
Thus the AP is 2, 7, 12…
For an A.P. show that \(a_p+a_{p+2q}=2a_{p+q} \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
…(1)
…(2)
From (1) and (2) we get
Find the sum of the 25 terms of an A.P. whose nth term is given by \(t_n=73n \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
How many terms are there in A.P. 7, 16, 25, ………., 349?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find the number of terms of the series: 5 + ( 8) + ( 11) + …………. + ( 230)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find the value of \(p \), if the numbers \(x, 2x + p, 3x + 6,\) are three consecutive terms of an A.P.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If the sum of first \(n \) terms of an A.P. is given by \(S_n=4n^23n \), find the nth term of the A.P.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The sum of the first n terms of an A.P. is given by \(S_n=3n^2n \). Determine the A.P. and its 25th term.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Required
In an A.P. the sum of first n terms is \(\dfrac{5n^2}{2}+\dfrac{3n}{2} \). Find its 20th term.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Second term
term