Question

Find the 12th term of the geometric sequence 8, 16, 32...

Answer 1

Answer:

16384

Step-by-step explanation:

We know that this is geometric sequence meaning we are multiplying the term before by a constant number.

We can see that 8 x 2 = 16 and 16 x 2 = 32. Meaning the number we are multiplying by is 2.

Terms:

We know that 8 is out first "term" so we don't multiply by anything. 16 is the second and we multiply 8 once to sixteen. 32 is the third and we multiply 8 twice by 2 to get to 32. We can see that the number of times we multiply is always 1 less that the term number.

We can write this equation. 8 x 2 ^ (n-1)

n is the term number.

This makes sense because we start with eight and multiply by two. We raise it to the n-1 power because we know we multiply 2 n-1 times to eight.

Answer:

Let's plug in our numbers!

8 x 2 ^ (12 - 1)

I use twelve because we're trying to figure out the 12th term.

8 x 2 ^ 11 = 16384

If you have a khan academy account I highly suggest you check out the unit about sequences in algebra 1! Good Luck

JoeLouis2

Answer 2

Answer:

a₁₂ = 16384

Step-by-step explanation:

The nth term of a geometric sequence is

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

Here a₁ = 8 and r = a₂ ÷ a₁ = 16 ÷ 8 = 2 , then

a₁₂ = 8 × $2^{11}$ = 8 × 2048 = 16384