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

Question:

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.

Solution:

Tn = (4n - 10)     [Given]
​T1 = (4 ⨯ 1 - 10) = -6
T2 = (4 ⨯ 2 - 10) = -2
T3 = (4 ⨯ 3 - 10) = 2
T4 = (4 ⨯ 4 - 10) = 6

Clearly, [ -2 - (-6)] = [2 - (-2)] = [6 - 2] = 4               (Constant)
So, the terms -6, -2, 2, 6,... forms an AP.

Thus, we have;
(i) First term = -6

(ii) Common difference = 4
(iii) T16 = a + (n -1)d  = a + 15d = ​- 6 + 15 ⨯ 4 = 54

 

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