Question

Find the next terms in a sequence
4, -20, 100, -500 _ _

Answer 1

Answer:2500

Step-by-step explanation:4*-5=-20

-20*-5=100

100*-5=-500

-500*-5=2500

Answer 2

The next terms in a sequence 4, -20, 100, -500 is 2500 and -12500

Solution:

Need to find the next two term in a sequence. 4 , -20 , 100 , -500 ,

Four terms are given need to determine fifth and sixth term.

So lets expand each term to understand the logic

`\begin{array}{l}{\text { First term }=4=4 * 1} \\\\ {\text { Second term }=-20=4 * 5 *(-1)} \\\\ {\text { Third term }=100=20 * 5 * 1} \\\\ {\text { Fourth term }=-500=100 * 5 *(-1)}\end{array}`

So logic says to get next term, multiply 5 by positive value of previous term and if the term is on even position then only multiply it by -1.

So fifth term as it is odd term, it will be positive value of fourth term multiplied by 5

=> 500 x 5 = 2500

And sixth term as it is even term, it will be positive value of fourth term multiplied by 5 multiplied by -1 = 2500 x 5 x (-1) = -12500

Hence next two terms in the given sequence 4 , -20 , 100 , -500 will be 2500 and -12500