Question

Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms

Answer 1

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

50, 46, 42, ... to 10 terms

Common difference of the A.P. (d)

`= a_2 - a_1`

= 46 - 50

= -4

 Number of terms (n) = 10

First term for the given A.P. (a) = 50

So using the formula we get

`S_10 = 10/2 [2(50) + (10 - 1)(-4)]`

= (5)[100 + (9)(-4)]

= (5)[100 - 36]

= (5)[64]

= 320

Therefore the sum of first 10 terms for the given A.P is 320