If second, sixth and eighteenth term of an ap are the consecutive term of gp. find the commom ratio

Common Ratio = First Term = Common Difference.

Step-by-step explanation:

The general term of AP is an = a + (n-1)d

So, the second term of AP is a2 = a + d

The sixth term of AP is a6 = a + 5d

The eighteenth term of AP is a18 = a + 17d

Now, the terms a2, a6 and a18 are in GP.

⇒

or,

By cross multiplying, we get

or,

Now, simplifying the above expression, we get that

or, r = a = d

Hence, the Common Ratio = First Term = Common Difference.

answer: a

step-by-step explanation: