Question

The n^th term of an Arithmetic Progression (A.P.) is given by the relation T_n = 6(7 – n)..

Find:

1. its first term and common difference
2. sum of its first 25 terms

Answer 1

Given, T_n = 6(7 – n)

a. For first term, put n = 1

Then, a₁ = 6(7 – 1)

= 6 × 6

= 36

For second term, put n = 2

Then a₂ = 6(7 – 2)

= 6 × 5

= 30

Then, common difference

∴ d = a₂ – a₁

= 30 – 36

= – 6

Hence, first term is 36 and common difference is - 6.

b. `S_n = n/2[2a + (n - 1)d]`

`S_25 = 25/2[2 xx 36 + (25 - 1)(-6)]`

= `25/2[72 - 144]`

= `25/2 xx (-72)`

S₂₅ = – 900