Question

the 3rd term of an arithmetic sequence is 17, and 9th is 83. what is the 1st term

Answer 1

This is an arithmetic progression (AP)
The general formula for any term is
\[a _{n} = a _{1} + (n-1)d\]

a(n) is the term you want, a1 is the first term and 'd' is the difference between terms

so for third term,
17 = a1+2d ===> a1 = 17-2d
for 9th term
83 = a1 + 8d

Solve the equation simultaneously
83= 17 - 2d +8d
6d = 66
d = 11

a1 = 17 -2(11) = -5

First term is -5