Question

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

Answer 1

Refer to explanation

Explanation:

The general formula for arithmetic progression is

`a_n=a_1+(n-1)*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*(n-1)`

for `n=4` we have that

`a_4=a_1+6=>a_1=3-6=>a_1=-3`

Finally we have that `a_n=-3+2*(n-1)`