Respuesta :
Answer:2500
Step-by-step explanation:4*-5=-20
-20*-5=100
100*-5=-500
-500*-5=2500
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
[tex]\begin{array}{l}{\text { First term }=4=4 \times 1} \\\\ {\text { Second term }=-20=4 \times 5 \times(-1)} \\\\ {\text { Third term }=100=20 \times 5 \times 1} \\\\ {\text { Fourth term }=-500=100 \times 5 \times(-1)}\end{array}[/tex]
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
