Advertisements
Advertisements
Question
First term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution: First term = a = 6, common difference = d = 3, S27 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]` - Formula
Sn = `27/2 [12 + (27 - 1)square]`
= `27/2 xx square`
= 27 × 45
S27 = `square`
Advertisements
Solution
It is given that,
First term (a) = 6
Common difference (d) = 3
Sn = `n/2 [bb(2a) + (n - 1)d]` - Formula
∴ S27 = `27/2 [2(6) + (27 - 1)bb((3))]`
= `27/2 (12 + 26 (3))`
= `27/2 (12 + 78)`
= `27/2 xx bb90`
= 1215
Hence, S27 = 1215.
RELATED QUESTIONS
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
In an AP Given a12 = 37, d = 3, find a and S12.
In an AP given a = 3, n = 8, Sn = 192, find d.
If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero.
A sum of ₹ 2800 is to be used to award four prizes. If each prize after the first is ₹ 200 less than the preceding prize, find the value of each of the prizes.
Sum of 1 to n natural numbers is 36, then find the value of n.
The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.
The sum of first 20 odd natural numbers is ______.
The common difference of the A.P. \[\frac{1}{3}, \frac{1 - 3b}{3}, \frac{1 - 6b}{3}, ...\] is ______.
Q.16
Q.20
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years.
Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
When the first term a, the number of terms n and the common difference d are known, which formula gives the sum of the first n terms of an Arithmetic Progression?
