Q10 of 47 Page 1

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.

Given that, first term = a = 8


Last term = l = 65


To find: common difference (d)


We know that sum of n terms of an AP = n (a + l)/2.


But given, sum of all terms = 730


∴ n (a + l)/2 = 730


⇒ n (8 + 65)/2 = 730


⇒ n (73)/2 = 730


⇒ n = (730 × 2)/73


⇒ n = 20 … (1)


We know that l = a + (n – 1) d.


Substituting the given values and n from (1), we get


65 = 8 + (20 – 1) d


⇒ 65 = 8 + 19d


⇒ 65 – 8 = 19d


⇒ 57 = 19d


⇒ d = 57/19


⇒ d = 3


The common difference d is 3.


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