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Starting with the third term, each term in Sequence S is one
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26 Mar 2018, 16:07
26 Mar 2018, 16:07
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Starting with the third term, each term in Sequence S is one-half the sum of the previous 2 terms. If the first 2 terms of Sequence S are 64 and 32, respectively, and the nth term is the first non-integer term of Sequence S, then n =
Drill 2
Question: 7
Page: 550
Question: 7
Page: 550
Show: :: OA
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Re: Starting with the third term, each term in Sequence S is one
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26 Mar 2018, 19:03
26 Mar 2018, 19:03
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Expert Reply
This is a sequence problem. Sometimes these can be made into easy equations, and sometimes the easiest way to solve them is to just follow the instructions for every successive piece of the sequence. In this case the algebra wouldn't be easy so let's just follow instructions. It'll never take too long because if it did take too long it wouldn't be on the test.
So the first two terms are 64 and 32. To get the next term, we're supposed to add these two and halve the result. Then just repeat until we don't get an integer. So the third term is (64 + 32)/2, or 48. Then we add the 2nd and 3rd terms and halve them to get the 4th term: (32 + 48)/2 = 40. Just keep going until we get to a non-integer answer. It helps to be systematic:
1st 64
2nd 32
3rd 48
4th 40
5th 44
6th 42
7th 43
We can see here that if we add 42 and 43 we'll get an odd number, which when divided by 2 will give us a .5 at the end rather than an integer, so the next term must be the nth term. In other words, n is 8.
So the first two terms are 64 and 32. To get the next term, we're supposed to add these two and halve the result. Then just repeat until we don't get an integer. So the third term is (64 + 32)/2, or 48. Then we add the 2nd and 3rd terms and halve them to get the 4th term: (32 + 48)/2 = 40. Just keep going until we get to a non-integer answer. It helps to be systematic:
1st 64
2nd 32
3rd 48
4th 40
5th 44
6th 42
7th 43
We can see here that if we add 42 and 43 we'll get an odd number, which when divided by 2 will give us a .5 at the end rather than an integer, so the next term must be the nth term. In other words, n is 8.
Re: Starting with the third term, each term in Sequence S is one
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04 Apr 2018, 16:06
04 Apr 2018, 16:06
Expert Reply
Explanation
Use brute force to solve this one: Write down the 2 given terms, find half the sum of the previous 2 terms, and repeat the process until you have a non-integer.
When you work it out, Sequence S should begin 64, 32, 48, 40, 44, 42, 43, 42.5; the first non-integer term is the 8th term, so n = 8.
Use brute force to solve this one: Write down the 2 given terms, find half the sum of the previous 2 terms, and repeat the process until you have a non-integer.
When you work it out, Sequence S should begin 64, 32, 48, 40, 44, 42, 43, 42.5; the first non-integer term is the 8th term, so n = 8.
