Geometric progression

Algebra Level pending

If the following sequence is a geometric progression , what is N N ?

1 , 4 , 16 , 64 , N 1, 4, 16, 64, N


The answer is 256.

Rex Holmes by Rex Holmes , 17, USA

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2 solutions

common ratio ⟹ \implies r = a 2 a 1 = a 3 a 2 = r = \large\dfrac{a_2}{a_1} = \large \dfrac{a_3}{a_2} = 4 \large 4

N = 64 ( 4 ) = N = 64(4) = 256 \boxed{\color{#D61F06}\large 256}

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Paola Ramírez
Aug 18, 2016

Each term is 4 4 times larger than its predecessor term, and as it is a progressive succession, 64 64 times 4 4 gives the next number in the sequence

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