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 three numbers in A.P. is –3, and their product is 8. Find the numbers
The sum of the first p, q, r terms of an A.P. are a, b, c respectively. Show that `\frac { a }{ p } (q – r) + \frac { b }{ q } (r – p) + \frac { c }{ r } (p – q) = 0`
The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?
If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.
Find the sum of all multiples of 7 lying between 300 and 700.
Which term of the AP ` 5/6 , 1 , 1 1/6 , 1 1/3` , ................ is 3 ?
Determine k so that (3k -2), (4k – 6) and (k +2) are three consecutive terms of an AP.
What is the 5th term form the end of the AP 2, 7, 12, …., 47?
If an denotes the nth term of the AP 2, 7, 12, 17, … find the value of (a30 - a20 ).
Write an A.P. whose first term is a and common difference is d in the following.
a = –3, d = 0
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals
A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find:
- the production in the first year.
- the production in the 10th year.
- the total production in 7 years.
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
The sum of first n terms of the series a, 3a, 5a, …….. is ______.
In an AP, if Sn = n(4n + 1), find the AP.
Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.
Solve the equation
– 4 + (–1) + 2 + ... + x = 437
