Question

1.45,46,70,141-------,1061.5.Fill up the blank.Ans;353.5
2.120,320 ---------,2070,5195,13007.5.fill up the blank.Ans;820

Answer 1

1. ans is 353.5 
logic is 45*1+1=46,
             46*1.5+1=70
             70*2+1=141
             141*2.5+1=353.5
2. all series follows x*2.5+20 so
               320*2.5+20=820

Answer 2

Answer:

The missing term in the series 45, 46,70, 141, .... ,1061.5 is 353.5

The missing term in the series 120, 320, .... ,2070, 5195, 13007.5 is 820

To find:  

The missing terms

Solution:

The first series is  45, 46, 70, 141, .... , 1061.5

Here the series is obtained by addition of one to the previous number along with the multiplication of the terms $\frac { 2 } { 2 } , \frac { 3 } { 2 } , \frac { 4 } { 2 } , \frac { 5 } { 2 } , \frac { 6 } { 2 }$

$45 \times \frac{2}{2}+1=45 \times 1+1=46$

$46 \times \frac {3}{2} +1=23 \times 3+1=70$

$70\times \frac {4}{2}+1 = 70\times 2+1 = 140+1=141$

$141\times \frac {5}{2}+1=70.5 \times 5+1=353.5\\\\353.5 \times \frac{6}{2}+1=353.5 \times 3+1=1061.5$

Hence, the missing term in the first series is 353.5

The given second series is  120, 320, …. , 2070, 5195, 13007.5

Here the series is obtained by the addition of 20 to the multiplication of the given number with the term 2.5

$120\times 2.5+20=300+20=320\\320 \times 2.5+20=800+20=820\\820 \times 2.5+20=2050+20=2070\\2070 \times 2.5+20=5175+20=5195\\5195 \times 2.5+20=12987.5+20=13007.5$

Hence, the missing term in the second series is 820.