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

Answer:

see the explanation

Step-by-step 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

$a_8=5(8)-2$

$a_8=38$