In a sequence, every term after the second term is twice the sum of the two proceding terms. The seventh term of the sequence is 8, and the ninth term is 24. What is the first term of the sequence?
2006-09-12 09:26:17 · 6 answers · asked by Anonymous in Education & Reference ➔ Homework Help
To start, never mind the first term, just work out the eighth one. The ninth term (24) is twice the sum of the eighth (we don't know yet) and the seventh (8), so the eighth and the seventh total 12, so the eighth is 4. See? Nothing else would make the ninth term be 24.
Now work out the sixth term from what you know about the seventh and eighth. Then work out the fifth term from what you know about the seventh and have worked out about the sixth. Keep going until you know the first and second terms.
Sorry, Chelsea, your answer is too simple and doesn't work.
2006-09-12 09:38:18 · answer #1 · answered by Anonymous · 0⤊ 0⤋
To get the 8th term:
2(8 + x) = 24 Divide by 2
8 + x = 12
x = 4 The 8th term is 4.
Now, to get the 6th term,
2(x + 8) = 4
x + 8 = 2
x = -6 The 6th term is -6
Etc,etc,etc. This is to long for me to sdo the whole thing for you, but I think that should help get you going.
2006-09-12 09:53:26 · answer #2 · answered by J 4 · 0⤊ 0⤋
First you have to go forward
(8+?)*2 = 24 ? has to be 4 so term 8 is 4
Next, use 4 and 8 to determine term 7
(?+8)*2 = 4 ? has to be -6 so term 6 is -6
Next, use -6 and 8 to determine term 5
(?+-6)*2 = 8 ? has to be 10 so term 5 is 10
Next, use 10 and -6 to determine term 4
(?+10)*2 = -6 ? has to be -13
Next, use -13 and 10 to determine term 3
(?+-13)*2 = 10 ? has to be 18
Next, use 18 and -13 to determine term 2
(?+18)*2 = -13 ? has to be -24.5
Next, use -24.5 and 18 to determine term 1
(?+-24.5)*2 =18 ? has to be 33.5
That is the procedure, check my math
2006-09-12 09:52:35 · answer #3 · answered by Dennis K 4 · 0⤊ 0⤋
work backward from 8: divided by 2, and get two numbers that can be added to get the answer (which was 4: like 2 and 2). the largest number of the 2 (the 2 used for the sum --*2=8--) will be the sixth term. good luck.
2006-09-12 09:30:06 · answer #4 · answered by Chelsea 2 · 0⤊ 1⤋
22.5 - but I'm not confident in that. This question makes me queasy, and I teach math. Sure you told us everything?
As for how I got it, you have to work backwards very carefully.
p.s. Chelsea is wrong because she's ignoring the 24 in the 9th position. You can't start from the 8. Each spot has one and only one possibility.
2006-09-12 09:35:55 · answer #5 · answered by ? 6 · 0⤊ 0⤋
try writing out an equation that will work with it, and then solve it from there.
2006-09-12 09:28:40 · answer #6 · answered by beckray 4 · 0⤊ 1⤋