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 term 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

S₂₀ = 2 × 20 – 3 × 20² 

= 40 – 1200 

= –1160