Question

1,2,5,14,...
..........................................................................

a(7)=?

Answer 1

Answer:

365

Step-by-step explanation:

Given Series is 1,2,5,14...

Difference is 1,3,9,27,...

Here, the ratio of all the adjacent terms is same and equal to r = 3.

a₁ = 1, a(n) = 3ⁿ⁻¹

Here, n = 7.

So,

a₅ = 3⁵⁻¹

    = 3⁴

    = 81.

Now,

Next common difference is 81.

Next common difference is 243(3⁵)

So, the series will be 1,2,5,14,41, 122(81+41),365(122+243).

Therefore, a(7) = 365.

Hope it helps!