Write the nth term rule for the sequence 1/2,3,11/2,8,21/2,...

Kelton Bailey

Kelton Bailey

Answered question

2022-09-03

Write the nth term rule for the sequence 1 2 , 3 , 11 2 , 8 , 21 2 , ...

Answer & Explanation

Matthew Benton

Matthew Benton

Beginner2022-09-04Added 9 answers

First decide whether it is an AP or GP.
Subtract consecutive terms.

11 2 - 3 = 5 1 2 - 3 = 2 1 2
3 - 1 2 = 2 1 2

There is the same difference, so it is an AP.

We have the first term, and d.
Sub into the general term.

T n = a + ( n - 1 ) d = 1 2 + 5 2 ( n - 1 )

T n = 1 2 + 5 n 2 - 5 2

T n = 5 n 2 - 2

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