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Which term of the AP : 3, 15, 27, 39, . . . will be 132 more t

Question

Which term of the AP : $3, 15, 27, 39, ..$ . will be $132$ more than its $5 4^{t h}$ term.

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Owen Discussed

Which term of the AP :

3, 15, 27, 39, ..

. will be

132

more than its

5 4^{t h}

term.

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Given A.P. is

3, 15, 27, 39, \dots

a = 3

d = a_{2} - a_{1} = 15 - 3 = 12

a_{54} = a + (54 - 1) d

= 3 + (53) (12)

= 3 + 636 = 639

Then,

132

more than its

5 4^{t h}

term is

132 + 639 = 771

We have to find the term of this A.P. which is

771

Let

n^{t h}

term be

771

\Rightarrow a_{n} = a + (n - 1) d

\Rightarrow 771 = 3 + (n - 1) 12

\Rightarrow 768 = (n - 1) 12

\Rightarrow (n - 1) = 64

∴ n = 65

Therefore,

6 5^{t h}

term was

132

more than

5 4^{t h}

term.

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Question Text	Which term of the AP : $3, 15, 27, 39, ..$ . will be $132$ more than its $5 4^{t h}$ term.
Answer Type	Text solution:1
Upvotes	150