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The formula for nth term of an arithmetic progression is aₙ = a + (n - 1) d .

Here, aₙ is the nth term, a is the first term, d is the common difference and n is the number of terms.

Given AP is 3, 15, 27, 39.

First term a = 3

Second term a + d = 15

d = 15 - 3 = 12

54th term of the AP is

a₅₄ = a + (54 - 1)d

= 3 + 53 × 12

= 3 + 636

= 639

Let nth term of AP be 132 more than 54th term

We get, 132 + 639 = 771

aₙ = 771

aₙ = a + (n - 1)d

771 = 3 + (n - 1)12

768 = (n - 1)12

(n - 1) = 64

n = 65

Therefore, the 65th term will be 132 more than the 54th term.

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Answer:

The formula for nth term of an arithmetic progression is aₙ = a + (n - 1) d .

Here, aₙ is the nth term, a is the first term, d is the common difference and n is the number of terms.

Given AP is 3, 15, 27, 39.

First term a = 3

Second term a + d = 15

d = 15 - 3 = 12

54th term of the AP is

a₅₄ = a + (54 - 1)d

= 3 + 53 × 12

= 3 + 636

= 639

Let nth term of AP be 132 more than 54th term

We get, 132 + 639 = 771

aₙ = 771

aₙ = a + (n - 1)d

771 = 3 + (n - 1)12

768 = (n - 1)12

(n - 1) = 64

n = 65

Therefore, the 65th term will be 132 more than the 54th term.

Step-by-step explanation:

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