Question 704501: What is the next two numbers in this sequence, 4,9,7,14,10,19,13,24,16,29
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Look at the odd numbered terms (in red)
4,9,7,14,10,19,13,24,16,29
Going from 4, to 7, to 10, etc tells us we're adding 3 to each term. This is because 4+3 = 7, 7+3 = 10, etc.
So part of the rule is this: if n is an odd number, then you use the rule: an = 3n+1 where n starts at n = 1. This rule only works if n is odd though.
If n is even, then we have this sequence (look at the above sequence, but instead of the red terms, focus on the black terms): 9, 14, 19, 24, 29
Now we're adding 5 to each term. So the rule is: if n is even, then use the formula an = 5n+4
So in the end, we have this rule
If n is odd, use the formula an = 3n+1, where n starts at n = 1
If n is even, use the formula an = 5n+4, where n starts at n = 2
That completes the entire sequence because any number is either even or odd.
The next term would be odd, so use the odd formula: 3n+1 = 3(6)+1 = 19. So the next term after 29 is 19
The term after that is even, so use 5n+4 = 5(6)+4 = 34.
So the next two terms are: 19 and 34
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Thanks,
Jim
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