Question

MATHEMATICS: The 5 and 11 terms of an Arithmes Progression (AP) are 13 and 31 respectively. Find the sum of its first term and common difference!​

Answer 1

`a_1 = 1\\d = 3`

Explanation:

The nth term of an arithmetic progression is
`a_n = a_1 + (n - 1)d`.
You are given that
`a_5 = 13` and
`a_(11) = 31`.

Therefore, we can solve the following system of equations to get the first term, as well as the difference.

`-\begin{cases}a_1 + 4d = 13\\a_1 + 10d = 31\end{cases}\\\\\to 6d = 18\\\to d = 3\\\\\text{Substitute d = 3 into one of the equations to find }a_1\text{:}\\a_1 + 4 * 3 = 13\\a_1 + 12 = 13\\\to a_1 = 1`