Question

-Find the missing term in the following series? 0,2,9,?,50,90,147

Answer 1

Answer is 24.

Step-by-step explanation:

0 ,2, 9, ?, 50, 90, 147.

0,2,9,24,50,90,147

diff b/w two terms

2-0=2,

9-2=7,

24-9=15,

50-24=26,

90-50=40,

147-90=57,

The new series : 2,7, 15, 26, 40, 57

diff & new series: 5, 8, 11, 14, 17

diff : 3, 3, 3, 3

Answer 2

• The missing term in the given series is equal to 24 .

To Find :- The missing term in the following series :- 0,2,9,?,50,90,147

Solution :-

Let us assume that, the missing term in given series is equal to x .

Since all terms of given series are increasing in random order . Using difference of difference method we get :-

→ 2 - 0 = 2

→ 9 - 2 = 7

→ x - 9 = (x - 9)

→ 50 - x = (50 - x)

→ 90 - 50 = 40

→ 147 - 90 = 57

again finding difference of difference we get,

→ 7 - 2 = 5

→ (x - 9) - 7 = (x - 16)

→ (50 - x) - (x - 9) = (59 - 2x)

→ 40 - (50 - x) = (x - 10)

→ 57 - 40 = 17

again finding difference of difference we get,

→ (x - 16) - 5 = (x - 21)

→ (59 - 2x) - (x - 16) = (75 - 3x)

→ (x - 10) - (59 - 2x) = (3x - 69)

→ 17 - (x - 10) = (27 - x)

again finding difference of difference we get,

→ (75 - 3x) - (x - 21) = (96 - 4x)

→ (3x - 69) - (75 - 3x) = (6x - 144)

→ (27 - x) - (3x - 69) = (96 - 4x)

Here, as we can see that, consecutive difference is same . Therefore, we can conclude that,

→ (96 - 4x) = (6x - 144) - (96 - 4x)

comparing first two difference,

→ (96 - 4x) = (6x - 144)

→ 6x + 4x = 96 + 144

→ 10x = 240

dividing both sides by 10,

→ x = 24 (Ans.)

Hence, the missing term in given series is equal to 24 .

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