Q3 of 67 Page 74

If the 7th and the 13th terms of an arithmetic progression are 34 and 64 respectively, then its 18th term is :

Let the first term be a and common difference be d.
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’



⇒ a7 = a + (7 - 1)d
⇒ 34 = a + 6d … (i)


⇒ a13 = a + (13 - 1)d
⇒ 64 = a + 12d …(ii)


On solving eq. (i) and (ii), we get :
a = 4 and d = 5


⇒ a18 = a + (18 - 1)d
⇒ a18 = 4 + 17 × 5
⇒ a18 = 4 + 85
⇒ a18 = 89

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