Question 815181: Dear Team
can you please help to get answers on these 2 questions?
1.Select the option for “?” that continues the pattern in each question
2, 7, 26, 101, 400, ?
2.Select the option for “?” that continues the pattern in each question
7, 21, 8, 72, 9, ?
Found 2 solutions by rapaljer, Edwin McCravy:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! I see a pattern for the first set in which you take the given number and multiply by 4 and subtract 1, then multiply by 4 subtract 2, multiply by 4 subtract 3, mult by 4 and subtract 4, etc. Starting with 2, multiply by 4 subtract 1 giving you 7. Take 7, multiply by 4 and subtract 2 giving you 26. Mult 26 times 4 and subtract 3 giving you 101. Multi by 4 subtract 4 giving you 400. Next would be multiply by 4 and subtract 5 giving 1595.
For the second pattern, I'm not sure. You might try starting with 7 *3 = 21. Next, take 8*3^2= 72. Next, take 9*3^3=243. This might be a stretch, but it's all I can think of.
Happy Thanksgiving!! Please see my website for FREE math explanations, and practice tests. See www.mathinlivingcolor.com.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
2, 7, 26, 101, 400, ?
It's not a geometric sequence, but it goes up fast like
one, so let's see how close it is to one.
The ratios of each term to the preceding one are
7/2 = 3.5
26/7 = 3.714
101/26 = 3.885
400/101 = 3.960
Those ratios seem to be getting close to 4.
So let's investigate how close each term is to
being 4 times the preceding term
Term #1: 7 is close to 4×2 which is 8. It's just 1 less.
Term #2: 26 is close to 4×7 which is 28. It's just 2 less.
Term #3: 101 is close to 4×26 which is 104. It's just 3 less.
Term #4: 400 is close to 4×101 which is 404. It's just 4 less.
Aha. Now we see the pattern.
Each term is 4 times the preceding term minus the number of term.
So term #5 will be 4×400 = 1600. Then 1600-5 (the term number) = 1595
-----------------------------------------
7, 21, 8, 72, 9
It looks like the odd terms have the pattern 7,8,9,10,11,...
Term #1 is 7
Term #2 is 21 or 7×31, and 1 is half of 2, the term number
Term #3 is 8
Term #4 is 72 or 8×9 or 8×3², and 2 is half of 4, the term number
Term #5 is 9
So each odd term is the next term of 7,8,9,10,11,...
Then each even term is the preceding odd term times
3 raised to the power which is half the term number.
So term #6 is 9×3³ since 3 is half the term number 6,
and 9×3³ = 9×27 = 243.
Edwin
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