Question

Find the 7th term of the geometric sequence show below 7x, -7x^5, 7x^9,…

Answer 1

Answer:

7x^25 :)

Step-by-step explanation:

1: 7x,

2. 7x^5,

3. 7x^9,

4. 7x^13,

5. 7x^17,

6. 7x^21,

7. 7x^25

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Answer 2

Answer:

$7x^{25}$

Step-by-step explanation:

Given sequence: $7x, -7x^5, 7x^9$

General form of a geometric sequence:  $a_n=ar^{n-1}$

(where a is the first term and r is the common ratio)

$a_1=7x$

$a_2=-7x^5$

$a_3=7x^9$

To find the common ratio, divide one term by the previous term:

$r=\dfrac{a_2}{a_1}=\dfrac{-7x^5}{7x}=-x^4$

Therefore, substituting the found values of a and r into the formula:

$\implies a_n=(7x)(-x^4)^{n-1}$

To find the 7th term, substitute n = 7 into the formula:

$\begin{aligned}\implies a_7 & =(7x)(-x^4)^{7-1}\\ & = (7x)(-x^4)^6\\ & = (7x)(x^{24})\\ & = 7x^{25}\end{aligned}$