Question

Given the sequence 4, 6, 10, 18, 34, ..., find the explicit formula

Answer 1

Given sequence is 4, 6, 10, 18, 34, ...

Now we have to find explicit formula for that which can generage the terms of given sequence.

Most of the time given sequence are AP, GP or polynomial or may be exponential.

If the common difference between consecutive terms is equal then it will be AP (arithmetic)

6-4=2

10-6=4

common difference is not equal so that means given sequence is not AP.

Now let's check for GP where ratio of consecutive terms is always equal

6/4=3/2

10/6=5/3

again ratio is not equal so it is not a GP.

We may rewrite the given sequence as:

4, 6, 10, 18, 34, ...

= 2+2, 4+2, 8+2, 16+3, 32+2, ...

$= 2^2, 2^2+2, 2^3+2, 2^4+2, 2^5+2, ...$

we see that only exponent of 2 changes so we can write explicit formula as $2^n+2$ where n is a natural number

Hence final answer is $2^n+2$.

Answer 2

Answer:

66

Step-by-step explanation:

Po Ang sagot