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From the subsequent options, which term of the AP 8, 14, 20, 26,… will be 72 more than its 41st term?

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44th

53rd

25th

38th

answer is D.

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Detailed Solution

It is given that, 8, 14, 20, 26,… are in AP.
The first term is,

a = 8

.
The common difference is given by,

d = a 2 − a 1

d = 14 − 8

= 6
The nth term of an AP is,

a n = a + (n − 1)

The 41st term of the AP is,

a 41 = 8 + (41 − 1) 6 a 41 = 8 + 40 × 6 = 8 + 240 = 248

From the given information, the term is 72 more than its 41st term.
So,

a n = a 41 + 72

a n = 248 + 72 = 320

Now to find the nth term of an AP, substitute the known values in the formula,

a n = a + (n − 1) d

320 = 2 + 6 n 6 n = 320 − 2 n = 3186 n = 53

Hence option 4) is correct.

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