Question

16,40,100,250,?
23,29,47,75,?
Explain the answers.
In each of the following questions write which term in the sequence replaces the question mark. ​

Answer 1

answers are 625,110 respectively

Answer 2

(i) 16,40,100,250,625.

Missing term : 625

(ii) 23,29,47,75,110.

Missing term : 110

(i) For the first series,

The second term is found out by multiplying the first term by 5 and then dividing the result by 2.

So, m = 5n/2 where m and n are the second and first term respectively.

For 16, (i.e. n = 16)

m = (5 × 16)/2 = 80/2 = 40, which is the second term.

For 40, (now n = 40)

m = (5 × 40)/2 = 200/2 = 100, which is the third term.

For 100,

m = (5 × 100)/2 = 500/2 = 250, which is the fourth term.

For 250,

m = (5 × 250)/2 = 1250/2 = 625, which is the fifth and the required term.

Missing term is 625.

(ii) For second series,

The second term is obtained by adding the first term with the result obtained by multiplying the units and tens digits of the first no.

m = n + x × y ,  where m and n are the second and first term respectively and x and y are the tens and ones digit respectively.

For 23, ( n = 23, x = 2, y = 3)

m = 23 + (2×3) = 23 + 6 = 29, which is the scond term.

For 29, ( n = 29, x = 2, y = 9)

m = 29 + (2×9) = 29 + 18 = 47, which is the third term.

For 47,

m = 47 + (4×7) = 75, which is the fourth term.

For 75,

m = 75 + (7×5) = 75 +35 = 110, which is the fifth and the missing term.

So, missing term is 110.