Question

4,2.5,3.5,6.75,15.5,41.25,________ number series

Answer 1

Consider the given number series,

4, 2.5, 3.5, 6.75, 15.5, 41.25, ?

We have to determine the next term in the given series,

Observe the first term 4,

Second term = $(4 \times \frac{1}{2})+\frac{1}{2}$ = $2+0.5 = 2.5$

Third term = $(2.5 \times 1) + 1 = 3.5$

Fourth term = $(3.5 \times \frac{3}{2}) + \frac{3}{2} = 6.75$

Fifth term = $(6.75 \times 2)+2= 15.5$

Sixth term = $(15.5 \times \frac{5}{2}) + \frac{5}{2}= 41.25$

Seventh term = $(41.25 \times 3) + 3 = 126.75$

Therefore, the next term in the given number series is 126.75

Answer 2

Answer:

Consider the given number series,

4, 2.5, 3.5, 6.75, 15.5, 41.25, ?

We have to determine the next term in the given series,

Observe the first term 4,

Second term = (4 \times \frac{1}{2})+\frac{1}{2}(4×

2

1

)+

2

1

= 2+0.5 = 2.52+0.5=2.5

Third term = (2.5 \times 1) + 1 = 3.5(2.5×1)+1=3.5

Fourth term = (3.5 \times \frac{3}{2}) + \frac{3}{2} = 6.75(3.5×

2

3

)+

2

3

=6.75

Fifth term = (6.75 \times 2)+2= 15.5(6.75×2)+2=15.5

Sixth term = (15.5 \times \frac{5}{2}) + \frac{5}{2}= 41.25(15.5×

2

5

)+

2

5

=41.25

Seventh term = (41.25 \times 3) + 3 = 126.75(41.25×3)+3=126.75

Therefore, the next term in the given number series is 126.75