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## The fifth term of an arithmetic sequence is 23 and the 12th term is 72? Determine the first three terms of the sequence and the nth term

Question

The fifth term of an arithmetic sequence is 23 and the 12th term is 72? Determine the first three terms of the sequence and the nth term

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Mathematics
6 months
2021-07-24T19:04:37+00:00
2021-07-24T19:04:37+00:00 1 Answers
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## Answers ( )

Answer:the first term is a1

the distance between the numbers is d

we have:

a5 = a1 + 4d = 23

a12 = a1 + 11d = 72

so we have the equation:

a1 + 4d = 23

a1 + 11d = 72

=> a1 = -5

d = 7

=>

an = -5 + 7(n – 1) = 7n – 12with an = 7n – 12

=> a2 = 2

a3 = 9

so

the first three terms is -5; 2; 9