Question

The A.P. 8, 10, 12, ....... has 60 terms. Find the sum of the last 10 terms.

Answer 1

Given A.P. is 8, 10, 12, ......., 60 terms.

Number of terms (n) = 60

First term (a) = 8

Common difference (d) = 2

We need the sum of the last 10 terms, i.e.,

t₅₁ + t₅₂ + ..... + t₆₀

Use the nᵗʰ term formula:

t_n = a + (n − 1)d

Find the 60^th term:

t₆₀ = 8 + (60 − 1)(2)

t₆₀ = 8 + 59(2)

t₆₀ = 8 + 118

t₆₀ = 126

Find the 51^st term:

t₅₁ = 8 + (51 − 1)(2)

t₅₁ = 8 + 50(2)

t₅₁ = 8 + 100

t₅₁ = 108

Now, find the sum of the last 10 terms.

Formula for sum of n terms:

`S_n = n/2 (t_51 + t_60)`

`S_10 = 10/2(108 + 126)`

S₁₀ = 5 × 234

S₁₀ = 1170