Question

Write a recursive formula and an explicit formula for the following arithmetic sequence: -1,6,13,20,27

Answer 1

Answer:

Recursive formula is: $a_1=-1 ; \ \ a_n=a_{n-1}+7$

Explicit formula is: $a_n=7n-8$

Step-by-step explanation:

We need to find recursive formula and explicit formula for arithmetic sequence -1,6,13,20,27

In the given sequence First term a₁= -1

Common difference d = 7

Finding Recursive Formula

The recursive formula is of type:$a_1= First \ term$ and $a_n=a_{n-1}+d$

Since the First term a₁ is -1 and common difference d is 7 so, the recursive formula  for given arithmetic sequence will be:

$a_1=-1 ; \ \ a_n=a_{n-1}+7$

Finding Explicit Formula

The explicit formula is of type: $a_n=a_1+(n-1)d$

We have

First term a₁= -1

Common difference d = 7

So, explicit formula will be:

$a_n=-1+(n-1)7\\a_n=-1+7n-7\\a_n=7n-8$

So, explicit formula is: $a_n=7n-8$