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zimovet [89]
3 years ago
9

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

Mathematics
1 answer:
Schach [20]3 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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