Advertisements
Advertisements
Questions
In an AP, given a = 7, a13 = 35, find d and S13.
In an A.P. (with usual notations): given a = 7, a13 = 35, find d and S13.
Advertisements
Solution
Given that, a = 7, a13 = 35
As an = a + (n − 1) d,
∴ a13 = a + (13 − 1) d
35 = 7 + 12d
35 − 7 = 12d
28 = 12d
d = `28/12`
d = `7/3`
sn = `n/2[a+a_n]`
S13 = `n/2[a+a_13]`
= `13/2[7+35]`
= `(13xx42)/2`
= 13 × 21
= 273
RELATED QUESTIONS
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185
Find the sum of the following APs.
`1/15, 1/12, 1/10`, ......, to 11 terms.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.
The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
The first term of an AP is p and its common difference is q. Find its 10th term.
If (2p +1), 13, (5p -3) are in AP, find the value of p.
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
Write an A.P. whose first term is a and common difference is d in the following.
a = –1.25, d = 3
Two A.P.’s are given 9, 7, 5, ... and 24, 21, 18, ... If nth term of both the progressions are equal then find the value of n and nth term.
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
If the sum of first n terms of an A.P. is \[\frac{1}{2}\] (3n2 + 7n), then find its nth term. Hence write its 20th term.
If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is ______.
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
For an A.P., If t1 = 1 and tn = 149 then find Sn.
Activitry :- Here t1= 1, tn = 149, Sn = ?
Sn = `"n"/2 (square + square)`
= `"n"/2 xx square`
= `square` n, where n = 75
If a = 6 and d = 10, then find S10
Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find Sn.
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
