Question

How many terms of the A.P. 3 + 9 + 15 + ... has the sum 7500?

Answer 1

a = 3

d = 9 − 3

= 6

S_n = 7500

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

7500 = `n/2[2(3) + (n - 1)6]`

7500 = n[3 + (n - 1)3]

7500 = n[1 + 3n − 1]

7500 = 3n²

`7500/3` = n²

n² = 2,500

 n = `sqrt(50 xx 50)`

n = 50