Advertisements
Advertisements
Question
Find the sum of the following arithmetic progressions:
a + b, a − b, a − 3b, ... to 22 terms
Solution
In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,
`S_n = n/2 [2a +_ (n -1)d]`
Where; a = first term for the given A.P.
d = common difference of the given A.P.
n = number of terms
a + b, a − b, a − 3b, ... to 22 terms]
Common difference of the A.P. (d) = `a_2 - a_1`
= (a - b) -(a + b)
= a - b - a - b
= -2b
Number of terms (n) = 22
The first term for the given A.P. (a) = a + b
So, using the formula we get,
`S_22 = 22/2 [2(a + b) + (22- 1)(-2b)]`
`= (11)[2a + 2b + (21)(-2b)]`
`= (11)[2a + 2b - 42b]`
= 22a - 440b
Therefore the sum of first 22 terms for the give A.P is 22a - 440b
APPEARS IN
RELATED QUESTIONS
The sum of n terms of three arithmetical progression are S1 , S2 and S3 . The first term of each is unity and the common differences are 1, 2 and 3 respectively. Prove that S1 + S3 = 2S2
Find the sum of the following Aps:
9, 7, 5, 3 … to 14 terms
How many terms of the AP 63, 60, 57, 54, ….. must be taken so that their sum is 693? Explain the double answer.
Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.
Write the nth term of an A.P. the sum of whose n terms is Sn.
Q.18
Find the sum of first 10 terms of the A.P.
4 + 6 + 8 + .............
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
What is the sum of an odd numbers between 1 to 50?
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.
