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Find a probable next term for the sequence 9,20,39,72,125,204,315
Question
Find a probable next term for the sequence 9,20,39,72,125,204,315
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Mathematics
4 years
2021-07-28T05:53:06+00:00
2021-07-28T05:53:06+00:00 1 Answers
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Answers ( )
Answer:
464
Step-by-step explanation:
The first term is 9.
The difference between the second and first term = 20 – 9 = 11
The difference between the third and second term = 39 – 20 = 19
The difference between the fourth and third term = 72 – 39 = 33
The difference between the fifth and fourth term = 125 – 72 = 53
The difference between the sixth and fifth term = 204 – 125 = 79
The difference between the seventh and sixth term = 315 – 204 = 111
The differences are 11, 19, 33, 53, 79, 111
From the difference: 19 – 11 = 8, 33 – 19 = 14, 53 – 33 = 20, 79 – 53 = 26, 111 – 79 = 32
We can see from the first difference (8), if we add 6 we get 14, if we add another 6 we get 20, if we add 6 we get 26, if add 6 we get 32
We get the eight term using:
32 + 6 = 38
let x be the difference between the eight term and the seventh term, hence:
x – 111 = 38
x = 111 + 38
x = 149
Therefore:
eighth term – seventh term = 149
eighth term – 315 = 149
eighth term = 149 + 315
eighth term = 464
The next probable term is 464