Find specific terms of an arithmetic sequence given other terms. How many terms are there in the following finite arithmetic sequence? 7,3,-1,\cdots,-89

allhvasstH

allhvasstH

Answered question

2021-08-08

Find specific terms of an arithmetic sequence given other terms.
How many terms are there in the following finite arithmetic sequence?
7,3,1,,89
1) 23
2) 24
3) 25
4) 28
5) 30

Answer & Explanation

Malena

Malena

Skilled2021-08-09Added 83 answers

Step 1
Given arithmetic sequence,
7,3,1,..,89
n-th term formula is:
an=a1+(n1)d
Where,
a1=first term of the sequence=7
an=last term of the sequence=89
d=common difference=(a2a1)=(37)=4
n=number of terms=?
Step 2
Substitute all values in the formula and solve for n,
89=7+(n1)(4)
897=4(n1)
96=4(n1)
(n1)=(96)(4)
(n1)=24
n=25
Therefore, there are 25 terms in the sequence.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-07-06Added 2605 answers

Answer is given below (on video)

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