Question

Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,

Answer 1

In the given problem, we need to find the sum of the n terms of the given A.P. 5, 2, −1, −4, −7, ...,

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

For the given A.P. (5, 2, -1, -4, -7)

Common difference of the A.P. (d) =`a_2 - a_1`

= 2 - 5

= -3

Number of terms (n) = n

First term for the given A.P. (a) = 5

So, using the formula we get,

`S_n = n/2 [2(5) + (n -1)(-3)]`

`= n/2 [10 + (-3n + 3)]`

`= n/2 [10 - 3n + 3]`

`= n/2 [13 - 3n]`

Therefore, the sum of first n terms for the given A.P. is `n/2 [13 - 3n]`