Q7 of 67 Page 74

The first term and the last term of an arithmetic progression are 1 and 11 respectively. If the sum of its terms is 36, then its number of terms will be:

Given, first term a = 1, last term l = 11 and Sn = 36.
Since, nth term an is given by :
an = a + (n - 1)d


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



⇒ 11 = 1 + (n - 1)d
⇒ 10 = (n -1)d … (i)


Since the sum of n terms is
Sn =

⇒ 72 = n[ 2 + (n-1)d] …(ii)


From eq. (i) and (ii), we get,
⇒ 72 = n[ 2 + 10]
⇒ 72 = 12n
⇒ n = 6

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