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

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 \(=7−6=1\)

hence, common ratio of given series is 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

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 \(=7−6=1\)

hence, common ratio of given series is 1.