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The First and the Last Terms of an Ap Are 8 and 65 Respectively. If the Sum of All Its Terms is 730, Find Its Common Difference. - Mathematics

The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.

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Solution

Let a be the first term, d be the common difference and Tn be the last of the AP.
Given:
a = 8
Tn = 65
Sn = 730

We know:
Tn = a + (n − 1)d
⇒ 65 = 8 + (n − 1)d
⇒ 57 = (n − 1)d                   ...(i)

and `Sn=n/2(a+Tn)`

`730=n/2(8+65)`

`n/2=730/73`

n=2x10=20

On substituting n = 20 in (i), we get:
57 = (20 − 1)d
⇒ 57 = (19)d
⇒ d = 57/19=3
Thus, the common difference is 3.

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