Answer:
a₁₂ = 16384
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 8 and r = a₂ ÷ a₁ = 16 ÷ 8 = 2 , then
a₁₂ = 8 × [tex]2^{11}[/tex] = 8 × 2048 = 16384
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