Which number follows the pattern?

Find the next number which follows this sequence?
1 , 2 , 6 , 15 , 31 , 56 , 92 , ? \Large 1,2,6,15,31,56,92,?


The answer is 141.

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1 solution

Ashish Menon
May 23, 2016

The pattern starts with 1. The next number 1 + 1 2 = 2 1 + \color{#D61F06}{1^2} = 2 . The next number 2 + 2 2 = 6 2 + \color{#D61F06}{2^2} = 6 . The next number 6 + 3 2 = 15 6 + \color{#D61F06}{3^2} = 15 . The next number 15 + 4 2 = 31 15 + \color{#D61F06}{4^2} = 31 . The next number 31 + 5 2 = 56 31 + \color{#D61F06}{5^2} = 56 . The next number 56 + 6 2 = 92 56 + \color{#D61F06}{6^2} = 92 . ,So, we see the next number is obtained by consecutively adding the successive square to the previous number. So, the answer is 92 + 7 2 = 92 + 49 = 141 92 + \color{#D61F06}{7^2} = 92 + 49 = \color{#69047E}{\boxed{141}} .

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