Question

What is the explict rule for the sequence 12,22,32,42​

Answer 1

The explicit rule for given sequence is:

$a_n=2+10n$

Further explanation:

We have to determine first of all if the sequence is arithmetic or geometric.

• If the difference of two consecutive terms is same then the sequence is arithmetic sequence
• If the ratio of two consecutive terms is same then the sequence is geometric sequence

Given sequence is:

12,22,32,42​

$a_1=12\\a_2=22\\a_3=32\\.......\\Let\\d=Common\ difference\\d=a_2-a_1=22-12=10\\d=a_3-a_2=32-22=10$

The common difference is 10 which is same for all consecutive terms. So the sequence is an arithmetic sequence.

The general formula for arithmetic sequence is:

$a_n=a_1+(n-1)d\\Here,\\a_n\ is\ the\ nth\ term\\a_1\ is\ the\ first\ term\\d\ is\ the\ common\ difference$

Putting the values of a1 and d

$a_n= 12+(n-1)(10)\\a_n=12+10n-10\\a_n=2+10n$

The explicit rule for given sequence is:

$a_n=2+10n$

Keywords: Arithmetic sequence, Common Difference

Learn more about arithmetic sequence at:

• brainly.com/question/1522572
• brainly.com/question/2491745

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