# 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.

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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