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Mathematics

Which term of the list of the numbers 5, 2, -1, -4, …. is -55?

AP GP

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Answer

The above list is an A.P. with a = 5 and d = 2 - 5 = -3.

Let the nth term of the A.P. be -55 or, an = -55.

We know that

an = a + (n - 1)d

⇒ -55 = 5 + (n - 1) × (-3)
⇒ -55 = 5 - 3n + 3
⇒ -55 = 8 - 3n
⇒ 3n = 8 + 55
⇒ 3n = 63
⇒ n = 21.

Hence, the 21st term of the A.P. is -55..

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