Question

30,36,40,42,46,52,58,60,68

Answer 1

72, 76, 82, 88..........

Answer 2

The next in this sequence 30, 36, 40, 42, 46, 52, 58, 60, 68 is 72.

Solution:

Given: 30, 36, 40, 42, 46, 52, 58, 60, 68

Difference between 36 and 30 = 6

$6 \times 5=30 \text { while } 6 \times 6=36.$ Hence, the difference of two numbers i.e., 6 is multiplied by 5 to get 30 and multiplied by 6 (number next to 5) to get 36.  

Difference between 40 and 36 = 4

$4 \times 9=36 \text { while } 4 \times 10=40.$ Hence, the difference of two numbers i.e., 4 is multiplied by 9 to get 36 and multiplied by 10 (number next to 9) to get 40.  

Difference between 42 and 40 = 2

$2 \times 20=40 \text { while } 2 \times 21=42.$ Hence, the difference of two numbers i.e., 2 is multiplied by 20 to get 40 and multiplied by 21 (number next to 20) to get 42.  

Difference between 46 and 42 = 4

Difference between 52 and 46 = 6

Difference between 58 and 52 = 6

Difference between 60 and 58 = 2

Difference between 68 and 60 = 8  

$8 \times 7.5=60 \text { while } 8 \times 8.5=68.$ Hence, the difference of two numbers i.e.8 is multiplied by 7.5 to get 60 and multiplied by 8.5 (number next to 7.5) to get  68.  

To get the number after 68, we are to find the number and the difference  between 68 and that number is to be multiplied by the number and its  consecutive number.

$4 \times 17=68 \text { while } 4 \times 18=72.$ Hence, the difference of two numbers i.e.72 - 68 = 4. When 4 is multiplied by 17 we get 68 and multiplied by 18 (number next to 17) to get 72.