# How do you give a recursive formula for the arithmetic sequence where the 4th term is 3; 20th term is 35?

Refer to explanation

#### Explanation:

The general formula for arithmetic progression is

${a}_{n} = {a}_{1} + \left(n - 1\right) \cdot d$ where

${a}_{n}$ is the n-th term in the sequence
${a}_{1}$ is the first term in the sequence
$d$ is the common difference

We know that ${a}_{4} = 3$ and ${a}_{20} = 35$ so

a_20-a_4=(a_1+19d)-(a_1+3d)=16d=> 16d=32=>d=2

Hence the formula becomes
${a}_{n} = {a}_{1} + 2 \cdot \left(n - 1\right)$

for $n = 4$ we have that

${a}_{4} = {a}_{1} + 6 \implies {a}_{1} = 3 - 6 \implies {a}_{1} = - 3$

Finally we have that ${a}_{n} = - 3 + 2 \cdot \left(n - 1\right)$