Question

if the sequence t1,t2,t3,..... are in ap then the sequence t8,t12,t18....is​

Answer 1

The sequence t8, t12, t18 are not in A.P.

Step-by-step explanation:

Let the sequence t1, t2, t3, ........  are in A.P. is given by t1 = a, t2 = a + d, t3 = a + 2d and so on.

So, the first term of the A.P. is a and the common difference is d.

So, t8 = a + (8 - 1)d = a + 7d

t12 = a + (12 - 1)d = a + 11d and

t18 = a + (18 - 1)d = a + 17d.

So, t12 - t8 = 4d and t18 - t12 = 6d

Therefore, the sequence t8, t12, t18 are not in A.P. (Answer)

Answer 2

Step-by-step explanation:

If t₁ ,t₂ , t₃ are in AP then :