Question

What is the next term in the pattern 1000, 500, 250, 125, 62.5, ……

Answer 1

31.25

Explanation:

Firstly, we need to identify the pattern.

Pattern: every next number is obtained by dividing the previous number by 2.

1st number = 1000

2nd number = 1000/2 = 500

3rd number = 500/2 = 250

4th number = 250/2 = 125

5th number = 125/2 = 62.5

6th number = 62.5/ 2 = 31.25.

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It can be also solved using concept of geometric progression

In GP

any nth number is given by =
`ar^(n-1)`

where a is first number

r is the common ratio for the gp

r common ratio is calculated by = nth/(n-1)th

here r = 500/1000 = 1/2

a = 1000

next term which we need to find is 6th terms

Thus, 6th terms =
`1000*(1/2)^(6-1)`

`=1000/2^5`

=1000/32 = 31.25