Question

complete the series- 3,6,15,42,_,_.

Answer 1

add powers of 3 each time.
so,
First, you add 3^0, which is 1. You get 3

Then you add 3^1, which is 3. You get 3+3 = 6

Then you add 3^2, which is 9. You get 6+9=15

Then you add 3^3, which is 27. You get 15+27, which is 42.

Then you add 3^4, which is 81. You get 42+81, which is 123. The next number is 123.

Answer 2

The complete series is 3, 6, 15, 42, 123, 366.

Given,

The series:

3, 6, 15, 42, _, _.

To find,

Next terms or, complete the given series.

Solution,

It can be seen that here, the given series is

3, 6, 15, 42, _, _.

To find the next terms or, to complete the given series, we need to know the pattern being followed in the series.

Observing the series, we can see, that the series follows a pattern that the succeeding term is 3 less than thrice the preceding term.

Say, for example,

the preceding term is 'a', then, the next term will be "3a - 3".

Consider the first two terms 3 and 6, then

the succeeding term = 6,

preceding term = 3.

It can be seen that,

6 (succeeding term) = 3 × 3 (preceding term) - 3.

Similarly, the series is as follows,

3 = (first term)

3 × 3 - 3 = 9 - 3 = 6 (2nd term),

3 × 6 - 3 = 18 - 3 = 15 (3rd term),

3 × 15 - 3 = 45 - 3 = 42 (4th term).

Thus, the next terms will be

3 × 42 - 3 = 126 - 3 = 123, and

3 × 123 - 3 = 369 - 3 = 366.

⇒ complete series = 3, 6, 15, 42, 123, 366.

Therefore, the complete series is 3, 6, 15, 42, 123, 366.

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