Question

How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?

Answer 1

Here, we find that

15 – 18 = 12 – 15 = –3

Thus, the given series is an A.P. with first term 18 and common difference –3.

Let the number of terms to be added be 'n'.

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

`\implies 45 = n/2 [2(18) + (n - 1)(-3)]`

`\implies` 90 = n[36 – 3n + 3]

`\implies` 90 = n[39 – 3n]

`\implies` 90 = 3n[13 – n]

`\implies` 30 = 13n – n²

`\implies` n² – 13n + 30 = 0

`\implies` n² – 10n – 3n + 30 = 0

`\implies` n(n – 10) – 3(n – 10) = 0

`\implies` (n – 10)(n – 3) = 0

`\implies` n – 10 = 0 or n – 3 = 0

`\implies` n = 10 or n = 3

Thus, the required number of terms to be added is 3 or 10.