The general term of a sequence is given a_{n} = n + 5. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference, if it is geometric, find the common ratio.

nicekikah 2021-02-09 Answered
The general term of a sequence is given an=n+5.
Determine whether the sequence is arithmetic, geometric, or neither.
If the sequence is arithmetic, find the common difference, if it is geometric, find the common ratio.
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Expert Answer

Szeteib
Answered 2021-02-10 Author has 102 answers

Step 1
Given: an=n+5.
for finding given sequence is arithmetic or geometric we find first three terms then check that given series is A.P. or G.P.
for finding first three term we put n=1,2,3 respectively
Step 2
So,
a1=1+5=6
a2=2+5=7
a3=3+5=8
here, first three terms are 6,7 and 8.
now checking for arithmetic progression
we know that in arithmetic progression
2(middle term)=first term+third term
so, putting values and checking
2(7)=14 and 6+8=14
here, 2(middle term)=first tem+third term
so, given sequence is arithmetic progression
now we can find common difference
we know that common difference of A.P. is given by :(second term)(first term)
so, common ratio =76=1
hence, common ratio of given series is 1.

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