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2 years ago

NEED HELP ASAP OR I WILL FAIL

Mathematics

1 answer:

Ulleksa [173]2 years ago

5 0

Answer: 1.24 is the answer

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Read 2 more answers

In a geometric sequence, a4 = 54 and a7 = 1,458. what is the 12th term? <br><br> answer: B) 354,294

slamgirl [31]

Option B:

The 12th term is 354294.

Solution:

Given data:

$a_4=54$ and $a_7=1458$

To find $a_{12}:$

The given sequence is a geometric sequence.

The general term of the geometric sequence is $a_n=a_1\ r^{n-1}$ .

If we have 2 terms of a geometric sequence $a_n$ and $a_k$ (n > K),

then we can write the general term as $a_n=a_k\ r^{n-k}$ .

Here we have $a_4=54$ and $a_7=1458$ .

So, n = 7 and k = 4 ( 7 > 4)

$a_7=a_4\ .\ r^{7-4}$

$1458=54\ . \ r^3$

This can be written as

$$r^3=\frac{1458}{54}$

$$r^3=27$

$$r^3=3^3$

Taking cube root on both sides of the equation, we get

r = 3

$a_{12}=a_7\ .\ r^{12-7}$

$=1458\ .\ r^5$

$=1458\ .\ 3^5$

$a_{12}=354294$

Hence the 12th term of the geometric sequence is 354294.

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