Find the sum of first n terms of an AP whose nth term is (5 – 6n). H

1.	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» Given: a_n = 5 – 6n Find some of the terms of AP: Put n = 1, we get a₁ = – 1 = first term Put n = 2, we get a₂ = – 7 = second term Common difference = d = a₂ – a₁ = – 7 – (-1) = – 6 Sum of first n terms: S_n= n/2 [2a + (n – 1)d] = n/2[- 2 + (n – 1)(-6)] = n(2 – 3n) sum of first 20 terms: S₂₀ = 20/2[2(-1) + (20 – 1)(-6)] = 10 [ – 2 – 114] = – 1160 Sum of its first 20 terms of AP is -1160.

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»

Given: a_n = 5 – 6n

Find some of the terms of AP:

Put n = 1, we get a₁ = – 1 = first term

Put n = 2, we get a₂ = – 7 = second term

Common difference = d = a₂ – a₁ = – 7 – (-1) = – 6

Sum of first n terms:

S_n= n/2 [2a + (n – 1)d]

= n/2[- 2 + (n – 1)(-6)]

= n(2 – 3n)

sum of first 20 terms:

S₂₀ = 20/2[2(-1) + (20 – 1)(-6)]

= 10 [ – 2 – 114]

= – 1160

Sum of its first 20 terms of AP is -1160.