Question

Find the sum of first 25 terms of the A.P. whose nth term is given by a_n = 5 + 6n. Also, find the ratio of 20^th term to 45^th term.

Answer 1

Given that,

`\implies` a_n = 5 + 6n

We have,

`\implies` a₁ = 5 + 6(1) = 11

`\implies` a₂ = 5 + 6(2) = 17

So, a = 11, d = 6

Sum of first 25 terms = `n/2(2a + (n - 1)d)`

= `25/2[2(11) + (25 - 1)6]`

= `25/2[22 + 144]`

= `25/2[166]`

= 2075

Now, a₂₀ = a + 19d

= 11 + 19(6)

= 125

`\implies` a₄₅ = a + 19d

= 11 + 44(6)

= 275

Required ratio = `a_20/a_45`

= `125/275`

= `5/11`

Ratio is 5:11.