If `a_(1),a_(2),a_(3),a_(4)` and `a_(5)` are in AP with common difference `ne 0,` find the value of `sum_(i=1)^(5)a_(i) " when " a_(3)=2`.

Explanation

To solve the problem, we need to find the value of the sum \( S = a_1 + a_2 + a_3 + a_4 + a_5 \) given that \( a_3 = 2 \) and the terms \( a_1, a_2, a_3, a_4, a_5 \) are in an arithmetic progression (AP) with a common difference \( d \neq 0 \).

### Step-by-Step Solution:

1. **Understanding the Terms in AP**:
In an arithmetic progression, the terms can be expressed in terms of the first term \( a_1 \) and the common difference \( d \):
- \( a_1 = a_1 \)
- \( a_2 = a_1 + d \)
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