Write a rule for a geometric sequence that has -6 as its first term and a common ratio of 2. What is the tenth term of this sequ

Question

2 years ago

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Write a rule for a geometric sequence that has -6 as its first term and a common ratio of 2. What is the tenth term of this sequ

ence?
A) A(n) = 2 * -6^10-1; -20,155,392
B) A(n) = -6 * 2^n; -6144
C) A(n) = -6 * 2^n-1; -3072
I need this Answered ASAP, Thank you

Mathematics

1 answer:

slega [8] · Answer 1 · 2022-06-08T09:35:06+03:00

The general form of the geometric sequence is $a_{n} = a_{1} (r) ^{n-1}$ , where a sub n is the number term you're looking for (we're looking for the tenth term). a sub 1 is the first term in the sequence (ours is -6), r is the common ratio, and n-1 is the numbered term you're looking for minus 1. Our formula then looks like this: $a_{10} =-6(2) ^{10-1}$ . Simplify it to $a_{10} =-6(2)^9$ . Take 2 to the 9th power then multiply it by -6 to get -3072. C is your answer.