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Step2247 [10]
4 years ago
6

Consider the sequence: 3, 8, 13, 18, 23, ...The recursive formula for this sequence is:an = an-1 + 5In a COMPLETE sentence, expl

ain what an and an-1 represent in the formula. Then find a8 . What do you need to know in order to find a8 ?
Mathematics
1 answer:
Leona [35]4 years ago
5 0

Answer:

see the explanation

Step-by-step explanation:

we know that

In an <u><em>Arithmetic Sequence</em></u> 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

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