Write the explicit formula for the sequence below and use it to find the 16th term: 6, -24, 96, -384, . . .

Question

Question

Write the explicit formula for the sequence below and use it to find the 16th term:
6, -24, 96, -384, . . .

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Mathematics Diễm Thu 3 years 2021-09-03T05:19:36+00:00 2021-09-03T05:19:36+00:00 1 Answers 18 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

Answer*

minhkhang · Answer 1 · 2021-09-03T05:20:48+00:00

Given:

The sequence is:

$6, -24, 96, -384,...$

To find:

The explicit formula for the given sequence and then find the 16th term.

Solution:

We have,

$6, -24, 96, -384,...$

The ratio between two consecutive terms are:

$\dfrac{-24}{6}=-4$

$\dfrac{96}{-24}=-4$

$\dfrac{-384}{96}=-4$

The given sequence has a common ratio. So, the given sequence is a geometric sequence with first term 6 and common ratio $-4$ .

The explicit formula of a geometric sequence is:

$a_n=ar^{n-1}$

Where, a is the first term and r is the common ratio.

Putting $a=6, r=-4$ in the above formula, we get

$a_n=6(-4)^{n-1}$

We need to find the 16th term. So, put $n=16$ in the above formula.

$a_n=6(-4)^{16-1}$

$a_n=6(-4)^{15}$

$a_n=6(-1073741824)$

$a_n=-6442450944$

Therefore, the explicit formula for the given sequence is $a_n=6(-4)^{n-1}$ and 16th term of the given sequence is $-6.442450944$ .