Question

Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of its first 20 terms.

Answer 1

Let a_n be the nth term of the AP. 

∴ a_n  = 5-6n

Putting n = 1,we get
First term, a = a₁ = 5-6 × 1 = -1  
Putting n = 2,we get
a₂ = 5-6 × 2 = -7 

Let d be the common difference of the AP.

∴ d = a₂ - a₁ = -7 - (-1) = -7 + 1 =-6 

Sum of first n tern of the AP,  S_n 

`= n/2 [ 2 xx (-1) + (n-1) xx (-6) ]            {s_n = n/2 [ 2a +(n-1) d]}`

`=n/2 (-2 - 6n +6)`

=n(2 -3n)

= 2n -3n²

Putting n = 20,we get

` s_20 = 2 xx 20- 3 xx20^2 = 40- 1200 = -1160`