Mathematics
Which term of the arithmetic progression 3, 15, 27, 39, …… will be 132 more than its 54th term ?
AP GP
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Answer
A.P. = 3, 15, 27, 39, ……
First term (a) = 3
Common difference (d) = 15 - 3 = 12.
By formula,
an = a + (n - 1)d = 3 + 12(n - 1)
= 3 + 12n - 12
= 12n - 9.
Let nth term of A.P. be 132 more than 54th term.
⇒ an = a54 + 132
⇒ 12n - 9 = a + (54 - 1)d + 132
⇒ 12n - 9 = 3 + 53 × 12 + 132
⇒ 12n - 9 = 3 + 636 + 132
⇒ 12n - 9 = 771
⇒ 12n = 771 + 9
⇒ 12n = 780
⇒ n = = 65.
Hence, 65th term of A.P. is 132 more than 54th term.
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