Question

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

Answer 1

Answer:

$T_{12} = 354294 + 354294i$

Step-by-step 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 $T_{12} = 354294 + 354294i$