Q12 of 47 Page 1

The first term of an A.P. is 5, the last term is 45 and the sum of all its terms is 400. Find the number of terms and the common difference of the A.P.

First term of AP, a = 5


Let no of terms be 'n' and common difference is 'd'


Last term of AP, an = 45


Given, sum of n terms = 400


And we know, sum of an AP if first term(a) and last term(an) is given,



Putting the values, we get,



⇒ 800 = 50n


⇒ n = 16


i.e. 16 terms are there and 16th term is last and equal to 45


Also, we know,


nth term of an AP,


Where, a and d are first term and common difference, respectively.


As, a16 = 45


⇒ a + 15d = 45


⇒ 5 + 15d = 45


⇒ 15d = 40



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