Sequence

Level 1

Problem: 12, 28, 48, 72, ....., 132 What is the appropriate number in the gap?

99 98 100 97

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2 solutions

Mahdi Raza
May 13, 2020

12 + 16 28 + 20 48 + 24 72 + 28 100 + 32 132 12 \quad \underrightarrow{{\color{#3D99F6}{+16}}} \quad 28 \quad \underrightarrow{{\color{#3D99F6}{+20}}} \quad 48 \quad \underrightarrow{{\color{#3D99F6}{+24}}} \quad 72 \quad \underrightarrow{{\color{#3D99F6}{+28}}} \quad {\color{#D61F06}{\boxed{100}}} \quad \underrightarrow{{\color{#3D99F6}{+32}}} \quad 132

Chris Lam
Jul 18, 2014

Since the second differences are 4, using the rule for quadratic sequences, you can see that a n = 2 n 2 + 10 n a_{n} = 2n^{2}+10n </br> From there, we can just plug in 5 for n and get 100 as an answer.

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