nicekikah

2021-02-09

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.

Szeteib

Step 1
Given: ${a}_{n}=n+5$.
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,
${a}_{1}=1+5=6$
${a}_{2}=2+5=7$
${a}_{3}=3+5=8$
here, first three terms are 6,7 and 8.
now checking for arithmetic progression
we know that in arithmetic progression
$\text{2(middle term)}=\text{first term}+\text{third term}$
so, putting values and checking
$2\left(7\right)=14$ and $6+8=14$
here, $\text{2(middle term)}=\text{first tem}+\text{third term}$
so, given sequence is arithmetic progression
now we can find common difference
we know that common difference of A.P. is given by :$\text{(second term)}-\text{(first term)}$
so, common ratio $=7-6=1$
hence, common ratio of given series is 1.

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