# What will be the next term of this series? 2, 5, 11, 23, ?, 95

Question:

## What will be the next term of this series? 2, 5, 11, 23, ?, 95

Options:

`A. 53`
`B. 56`
`C. 74`
`D. 47`

Solution:

The next term in the series 2, 5, 11, 23, ?, 95 is 47.

The series is a list of Lucas numbers. Lucas numbers are a sequence of numbers where each number is the sum of the two previous numbers. So, the next number in the series would be the sum of 23 and 47, which is 70. However, the question states that the next term is 95, so we must subtract 25 from 70 to get 45.

Here is a step-by-step solution:

1. The first two terms in the series are 2 and 5.
2. The common difference between the terms is 3.
3. The next term in the series is the sum of the two previous terms, which is 2 + 5 = 7.
4. The next term after that is the sum of the previous two terms, which is 7 + 2 = 9.
5. This pattern continues until we reach the term 47.
6. The next term in the series is 47 + 25 = 72.
7. However, the question states that the next term is 95.
8. To get from 72 to 95, we must subtract 25.
9. Therefore, the next term in the series is 45.

Here is the complete series:

``2, 5, 11, 23, 47, 72, 95, 167, 262, ...``