Question

Find t12 for a geometric sequence where t1=2+2i and r=3

Answer 1

`T_(12) = 354294 + 354294i`

Explanation:

Given

Geometric Sequence (GP)

`T_1 = 2 + 2i`

`r = 3`

Required

Determine T₁₂

The nth term of a GP is calculated as thus;

`T_n = ar^(n-1)`

In this case;

`n = 12`;
`r = 3` and
`a = T_1 = 2 + 2i`

Substitute these values in the above formula

`T_(12) = (2 + 2i) * 3^(12-1)`

`T_(12) = (2 + 2i) * 3^(11)`

`T_(12) = (2 + 2i) * 177147`

Open the bracket

`T_(12) = 177147 * 2 + 177147 * 2i`

`T_(12) = 354294 + 354294i`

Hence, the 12th term of the sequence is
`T_(12) = 354294 + 354294i`