Question

Find the 8th term of the geometric sequence 7,28,112

Answer 1

Answer:

• 7*4⁷ or 114688

Step-by-step explanation:

This is a GP with:

• The first term of a₁ = 7
• Common ratio r = 4

Use the nth term formula:

• aₙ = a₁rⁿ⁻¹
• a₈ = 7*4⁷ = 114688

Answer 2

Answer:

114688

Step-by-step explanation:

General form of a geometric sequence:

  $a_n=ar^{n-1}$

where:

• $a_n$ is the nth term
• a is the first term
• r is the common ratio

Given sequence:  7, 28, 112, ...

First term

From inspection of the given sequence, the first term is 7:

$\implies a=7$

Common ratio

To find the common ratio r, divide consecutive terms:

$\implies r=\dfrac{a_2}{a_1}=\dfrac{28}{7}=4$

Equation for the nth term

Substitute the found values of a and r into the formula to create an equation for the nth term:

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

8th term

To find the 8th term, substitute n = 8 into the found equation:

$\implies a_8=7(4)^{8-1}$

$\implies a_8=7(4)^7$

$\implies a_8=7(16384)$

$\implies a_8=114688$

Learn more about geometric sequences here:

https://brainly.com/question/27783194