Question

Get the general term for the sequence being your t3 = 11 and the t20 = 244.2

Answer 1

nth term =
`t_(n) = 7.639(1.2)^(n - 1)`

Explanation:

Let us assume that the given sequence is a G.P.

Now, if the first term of the G.P. is a and the common ratio is r, then

Third term =
`t_(3) = ar^(2) = 11` .......... (1) and

20th term =
`t_(20) = ar^(19) = 244.2` ........... (2)

Now, dividing equation (2) with equation (1) we get

`(ar^(19) )/(ar^(2) ) = (244.2)/(11) = 22.2`

⇒
`r^(17) = 22.2`

⇒ r = 1.2.

Hence, from equation (1) we get

a(1.2)² = 11

⇒ a = 7.639 (Approx.)

Therefore, the general term of the sequence i.e. nth term =
`t_(n) = 7.639(1.2)^(n - 1)` (Answer)