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4 years ago

Write the recursive formula then determine the next term of 3,10,24,52

Mathematics

1 answer:

Schach [20]4 years ago

7 0

Answer:

f[1] = 3
f[n] = 2·f[n-1] +4
108

Step-by-step explanation:

We observe that first differences of the given numbers are ...

10 -3 = 7

24 -10 = 14

52 -24 = 28

That is, each difference is 2× the previous one. This suggests an exponential relation that has a base of 2.

We notice that doubling a term doesn't give the next term, but gives a value that is 4 less than the next term. So, we can get the next term by doubling the previous one and adding 4.

Then our recursive relation is ...

f[1] = 3 . . . . the first term

f[n] = 2×f[n-1] +4 . . . . double the previous term and add 4

The next term is 2·52 +4 = 108.

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