Find the missing term in the series given below.2, 12, 36, 80, ?
Question
Find the missing term in the series given below.2, 12, 36, 80, ?
Solution
The given series is 2, 12, 36, 80, ?
This is a series of numbers where each term is obtained by adding a certain number to the cube of a natural number.
Let's break it down:
- The first term is 2, which is 1^3 + 1.
- The second term is 12, which is 2^3 + 4.
- The third term is 36, which is 3^3 + 9.
- The fourth term is 80, which is 4^3 + 16.
From this pattern, we can see that the nth term is given by n^3 + n^2.
So, the fifth term should be 5^3 + 5^2 = 125 + 25 = 150.
Therefore, the missing term in the series is 150.
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