Question

$\huge{\boxed{\boxed{\tt{\purple{Spammers\:Stay\:Away}}}}}$
Number series.
1. 10, 17.5, 32.5, 55, 85, ?
2. 6, 6, 18, 90, 630, ?
3. 2, 2, 5, 15.5, ?, 267.125
4. 0, 6, 24, 60, 120, ?​

Answer 1

Step-by-step explanation:

1.

10 = 10

17.5 = 10 + 7.5

32.5= 10 + 7.5 + 15

55= 10 + 7.5 + 15 + 22.5

85 = 10 + 7.5 + 15 + 22.5 + 30

Therefore, Next term will be: 10 + 7.5 + 15 + 22.5 + 30 + 37.5 = 122.5

2.

6

6 = 6 + 6×0

18 = 6 + 6×2

90 = 18 + 18×4

630 = 90 + 90×6

Therefore, 630 + 630×8 = 5670

3.

2 =

2 = 2×0.5 + 1

5 = 2 × 1.5 + 2

15.5 = 5 × 2.5 + 3

x = 15.5 × 3.5 + 4 = 54.25 + 4 = 58.25

4.

0 = 0³ - 0

6 = 2³ - 2

24 = 3³ - 3

60 = 4³ - 4

120 = 5³ - 5

Similarly, 6³ - 6 = 210

Answer 2

$\huge\bf\underline\purple{Solution\:1࿐}$

10 = 10

17.5 = 10 + 7.5

32.5= 10 + 7.5 + 15

55= 10 + 7.5 + 15 + 22.5

85 = 10 + 7.5 + 15 + 22.5 + 30

Therefore, Next term will be: 10 + 7.5 + 15 + 22.5 + 30 + 37.5 = $\bold\red{122.5}$

$\huge\bf\underline\purple{Solution\:2࿐}$

6 = 6 + 6×0

18 = 6 + 6×2

90 = 18 + 18×4

630 = 90 + 90×6

Therefore, 630 + 630×8 = $\bold\red{5690}$

$\huge\bf\underline\purple{Solution\:3࿐}$

2 = 2×0.5 + 1

5 = 2 × 1.5 + 2

15.5 = 5 × 2.5 + 3

x = 15.5 × 3.5 + 4 = 54.25 + 4 = $\bold\red{58.25}$

$\huge\bf\underline\purple{Solution\:4࿐}$

0 = 0³ - 0

6 = 2³ - 2

24 = 3³ - 3

60 = 4³ - 4

120 = 5³ - 5

Similarly, 6³ - 6 = $\bold\red{210}$