Question

1 of 3

Enter the next 3 terms from the geometric sequence below
3, 6, 12,...
T4=
T5 T6 =
10
T6 =

Answer 1

T4= 24 , T5= 48, T6= 96

Let the First term be a

a = 3

let the common ratio be r

`r = (T3)/(T2)`

where T2 and T3 are the second and third terms of the the geometric sequence respectively.

`r = (12)/(6) = 2`

Therefore r = 2

To find the next three term ie the fourth, fifth and sixth terms

`Tn = ar {}^(n - 1)`

`T4 = 3 * 2 {}^(4 - 1) \\ = 3 * 2 {}^(3) \\ = 3 * 8 = 24`

`T5 = 3 * 2 {}^(5 - 1) \\=3 * 2 {}^(4) \\= 3 *16\\=48`

`T6 = 3 * 2 {}^(6 - 1) \: \\=3 * 2 {}^(5) \\ = 3 * 32 \\= 96`