Mathematics
If the nth term of the A.P. 58, 60, 62, …… is equal to the nth term of the A.P. -2, 5, 12, ……., find the value of n.
AP
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Answer
nth term of the A.P. 58, 60, 62, ……
In above sequence,
60 - 58 = 2 and 62 - 60 = 2.
Hence, above sequence is an A.P. with common difference = 2.
an = a + (n - 1)d
= 58 + (n - 1)2
= 58 + 2n - 2
= 2n + 56.
nth term of the A.P. -2, 5, 12, …….
In above sequence,
5 - (-2) = 7 and 12 - 5 = 7.
Hence, above sequence is an A.P. with common difference = 7.
an = a + (n - 1)d
= -2 + (n - 1)7
= -2 + 7n - 7
= 7n - 9.
Since, nth term of the A.P. 58, 60, 62, …… is equal to the nth term of the A.P. -2, 5, 12, …….
∴ 2n + 56 = 7n - 9
⇒ 7n - 2n = 56 + 9
⇒ 5n = 65
⇒ n = 13.
Hence, n = 13.
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