Question

3,8,18,38,78 what is the last number

Answer 1

Given:

Series 3,8,18,38,78

To Find:

The last number

Solution:

The logic behind the given series is as follows:

First term = 3

Second term = 3+5

                      = 8

Third term = 8+10

                  = 18

Fourth term = 18+20

                    = 38

Fifth term = 38+40

                = 78

So, the next term will be

78 + 160 = 158

Hence,  the last number is 158

Answer 2

Given sequence of numbers are 3, 8, 18, 38, 78.

We have to find the next number of the sequence.

We need to observe the relation between the sequence of numbers to find the next number of that sequence.

Let,

$a0 = 3 \\ a1 = 8 \\ a2 = 18 \\ a3 = 38 \\ a4 = 78$

Now, let us observe the difference of these numbers.

$a1 - a0 \\ = 8 - 3 \\ = 5$

For the next two numbers difference is

$a2 - a1 \\ = 18 - 8 \\ = 10$

For the next two terms of the sequence,

$a3 - a2 \\ = 38 - 18 \\ = 20$

Next two terms,

$a4 - a3 \\ = 78 - 38 \\ = 40$

If we observe all the differences,

5, 10, 20, 40.

Each difference is twice of the previous difference.

Hence, the next difference of the sequence,

i.e,

$a5 - a4 = 2 \times 40 \\ a5 - 78 = 80 \\ a5 = 80 + 78 \\ a5 = 158$

Therefore, next term of the sequence is 158.

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