Question

4, 5, 9, 18, 34,
What is the next number

Answer 1

Answer:

59

Step-by-step explanation:

4 + 1² = 5 + 1 = 5

5 + 2² = 5 + 4 = 9

9 + 3² = 9 + 9 = 18

18 + 4² = 18 + 16 = 34

34 + 5² = 34 + 25 = 59

Answer 2

Answer:

Answer: Next number in series = 59

Step-by-step explanation:

The given series: 4, 5, 9, 18, 34, ……

Let us take the differences between the consecutive numbers. We get

First difference : 1, 4, 9, 16, 25,……..

Second difference: 3, 5, 7, 9, …..…

Third difference: 2, 2, 2, 2, 2, …….

We stop with the third difference because we see a pattern here. The pattern is all the differences are a constant and equal to 2. We then work backwards.

The next number after 7 in second difference will be 7 + 2 = 9

The next number after 16 will be 16 + 9 = 25

If X is the number that would come next to 34, we must have the equality

X - 34 = 25

Transposing -34 to right and changing sign,

X = 34 + 25 = 59

∴ The required number that comes after 34 is 59 (Answer).

Aliter,

From the given series, we observe that

5–4 = 1 = 1²

9 - 5 = 4 =2²

18-9 = 9=3²

34–18=16=4²

Following this pattern, we should have

X - 34 = 5²

where X is the unknown number that comes after 34.

∴ X = 34 + 25 (By transposition)

Or, X = 59 (Answer)