Find the function if the second term in an arithmetic sequence is 5 and the fifth term is 68

propappeale00 2022-10-22 Answered
Find the function if the second term in an arithmetic sequence is 5 and the fifth term is 68
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Answers (1)

scranna0o
Answered 2022-10-23 Author has 16 answers
The general term of an arithmetic sequence is given by the formula:
a n = a + d ( n - 1 )
where a is the initial term and d the common difference.
We find:
3 d = ( a + 4 d ) - ( a + d ) = a 5 - a 2 = 68 - 5 = 63
Dividing both ends by 3 we get:
d = 21
Then:
a 1 = a = ( a + d ) - d = a 2 - d = 5 - 21 = - 16
So the formula for the general term can be written:
a n = - 16 + 21 ( n - 1 ) = 21 n - 37
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