Question

What is the next term of the geometric sequence?
128, 32, 8,

Answer 1

The next term of the geometric sequence is 2

GIVEN:- geometric sequence = 128, 32, 8,

TO FIND:- Next term in the geometric sequence

SOLUTION:-

• In mathematics, a geometric sequence is a chain of numbers that follow a specific pattern.
• Each element in a sequence is called a term.

According to the question we need to find the next term

The pattern which the geometric sequence is following is

• Each term is divided by 4 to give the value of the next term in the geometric sequence

$128 \\ \frac{128}{4} = 32 \\ \frac{32}{4} = 8 \\ \frac{8}{4} = 2$

Hence, The next term of the geometric sequence is 2

#SPJ2

Answer 2

The next term is 2

Given:

128, 32, 8 .. is geometric sequence

To find:

Next term in given GP

Solution:

Given GP is 128, 32, 8...

Where first term a = 128

common ration = a₂/a₁ = $\frac{32}{128}$ = $\frac{1}{4}$

⇒ common ratio, r = 1/4

In GP nth term = $ar^{n-1}$  

Here we need to find 4th term  a₄ = $ar^{4-1}$ = ar³

⇒ $128(\frac{1}{4^{3} } )$ = $128(\frac{1}{64 } )$ = 2

Therefore, 4th term of GP = 2

#SPJ2