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Mathematics

Find the 10th and nth terms of the list of numbers 5, 25, 125, …

AP GP

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Answer

The given list of numbers 5, 25, 125 …. is a G.P. with first term a = 5 and r = 5.

By formula, an = arn - 1

a10=5(5)10−1=5(5)9=510.an=5(5)n−1=5×5n×5−1=5n.a{10} = 5(5)^{10 - 1} = 5(5)^9 = 5^{10}. \\[1em] an = 5(5)^{n - 1} = 5 \times 5^n \times 5^{-1} = 5^n.

Hence, the 10th term is 510 and nth term is 5n.

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