Find the common ratio & the next three terms in the sequence. 2.-6, 18, -54, ... a Common Ratio: r= 3 Next 3 terms: 32, -64, 128 b Common Ratio: r = 5 Next 3 terms: 1250, 62…

Question

asked Feb 21, 2022 20.3k views

1 Answer

Badgy · Answer 1 · 2022-02-26T12:02:51+0000

Answer:

We conclude that:

Hence, option D is correct.

Explanation:

Given the geometric sequence

2, -6, 18, -54, ...

Here:

a_1=2

A geometric sequence has a constant difference 'r' and is defined by

$a_n=a_1\cdot \:r^(n-1)$

computing the differences of all the adjacent terms

$(-6)/(2)=-3,\:\quad (18)/(-6)=-3,\:\quad (-54)/(18)=-3$

The ratio of all the adjacent terms is the same and equal to

r=-3

now substituting
a_1=2 and
r=-3 in the nth term of the sequence

$a_n=a_1\cdot \:r^(n-1)$

now substituting n = 5 to determine the 5th term

$a_5=2\left(-3\right)^(5-1)$

$a_5=3^4\cdot \:2$

$a_5=2\cdot \:81$

a_5=162

now substituting n = 6 to determine the 6th term

$a_6=2\left(-3\right)^(6-1)$

$a_6=-2\cdot \:243$

a_6=-486

now substituting n = 7 to determine the 7th term

$a_7=2\left(-3\right)^(7-1)$

$a_7=2\cdot \:729$

a_7=1458

Therefore, we conclude that:

Hence, option D is correct.