Question

Consider the sequence: 3, 8, 13, 18, 23, ...The recursive formula for this sequence is:an = an-1 + 5In a COMPLETE sentence, explain what an and an-1 represent in the formula. Then find a8 . What do you need to know in order to find a8 ?

Answer 1

see the explanation

Explanation:

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant called the common difference

we have

`3, 8, 13, 18, 23,...`

Let

`a_1=3\\a_2=8\\a_3=13\\a_4=18\\a_5=23\\`

`a_2-a_1=8-3=5` ------>
`a_2=a_1+5`

`a_3-a_2=13-8=5` ------>
`a_3=a_2+5`

`a_4-a_3=18-13=5` ------>
`a_4=a_3+5`

`a_5-a_4=23-18=5` ------>
`a_5=a_4+5`

so

the common difference between consecutive terms is equal to 5

we can rewrite the formula as

`a_n=a_(_n_-_1_)+5` -----> given formula

For n > 1

where

an is the term that you want to find (position n)

a(n-1) is the known term position (n-1)

Find a_8

For n=8

`a_8=a_(_8_-_1_)+5`

`a_8=a_7+5`

I need to know a_7

or

we know that

The general formula for arithmetic sequence is equal to

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

where

an is the term that you want to find (position n)

a_1 is the first term

d is the common difference

n is the number of terms

we have

`a_1=3`

`d=5`

substitute

`a_n=3+5(n-1)`

`a_n=3+5n-5`

`a_n=5n-2`

so

For n=8

`a_8=5(8)-2`

`a_8=38`