Question

2) write a rule for the nth term find ago 8,21,34,47,60,...

Answer 1

The rule for the nth terms is: a_n=13n-5

Further explanation:

First of all we have to decide whether it is an arithmetic sequence or geometric sequence. It is decided based upon common difference or common ratio.

common difference is the difference between two consecutive terms of an arithmetic sequence while common ratio is the ratio between consecutive terms of a geometric sequence.

Here

$a_1=8\\a_2=21\\a_3=34\\a_4=47\\a_5=60.....$

Common difference:

$d=a_2-a_1=21-8=13\\a_3-a_2=34-21=13$

As the common difference is same, the given sequence is an arithmetic sequence

The general formula for arithmetic sequence is:

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

Here

a1=8

d=13

$a_n=8+(n-1)13\\=8+13n-13\\=13n-5$

The rule for the nth terms is: a_n=13n-5

Keywords: Arithmetic sequence, Common difference

Learn more about arithmetic sequence:

• brainly.com/question/2821386
• brainly.com/question/2860697

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