Q. 63.9( 26 Votes )

If the nth term of a progression is (4n - 10) show that it is an AP. Find its

(i) first term,

(ii) common difference, and

(iii) 16th term.

Answer :

nth term of the AP is (4n - 10).

For n = 1, we have a1 = 4 - 10 = - 6


For n = 2, we have a2 = 8 - 10 = - 2


For n = 3, we have a3 = 12 - 10 = 2


For n = 4, we have a4 = 16 - 10 = 6, and so on.


a4 - a3 = a3 - a2 = a2 - a1 = 4 = constant.


the given progression is an AP.


Hence, (i) Its first term = a = - 6


(ii) common difference = 4


(iii) To find :16th term


a16 = a + (16 - 1)d


a16 = - 6 + 15 × 4 = 54


16th term of the given AP is 54.


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