If `n` arithemetic means are inserted between `20` and `80` such tht the ratio of first mean to the last mean is `1:3,` then find the value of `n`

Explanation

To solve the problem, we need to find the value of \( n \) when \( n \) arithmetic means are inserted between 20 and 80 such that the ratio of the first mean to the last mean is \( 1:3 \).

### Step-by-Step Solution:

1. **Identify the Terms**:
We have the first term \( a = 20 \) and the last term \( l = 80 \). We are inserting \( n \) arithmetic means between them.

2. **Determine the Total Number of Terms**:
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