Question

FIRST TERMS OF GEOMETRIC SEQUENCE 160 80 40

WHAT WOULD THE NEXT TWO SEQUENCE BE? N COULD U TELL ME HOW TO YOU GOT THE SEQUENCES?

Answer 1

The next two terms of the sequence are 20, 10

Solution:

The geometric equation is 160, 80, 40…..

The first term of the equation is
`a_(1)=160`.

Now the ratio between the numbers of the sequence
`r=\left((80)/(160)\right)=\left((1)/(2)\right)`

As we know that the nth term of the sequence
`a_(n)=a_(1) * r^(n-1)`

Hence,

`a_(4)=160 *\left((1)/(2)\right)^(4-1)`

`\rightarrow 160 *\left((1)/(2)\right)^(3)`

`\rightarrow160 *\left((1)/(8)\right) = 20`

`\mathrm{a}_(5)=160 *\left((1)/(2)\right)^(5-1)`

`\rightarrow160 *\left((1)/(2)\right)^(4)`

`\rightarrow160 *\left((1)/(16)\right) = 10`