Q10 of 47 Page 1

The first and last terms of an AP are 7 and 49 respectively. If the sum of all its terms is 420, find its common difference.

Given that, first term = a = 7


Last term = l = 49


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 = 420


∴ n (a + l)/2 = 420


⇒ n (7 + 49)/2 = 420


⇒ n (56)/2 = 420


⇒ 28n = 420


⇒ n = 420/28


⇒ n = 15 … (1)


We know that l = a + (n – 1) d.


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


49 = 7 + (15 – 1) d


⇒ 49 = 7 + 14d


⇒ 49 – 7 = 14d


⇒ 42 = 14d


⇒ d = 42/14


⇒ d = 3


The common difference d is 3.


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