How many terms are there in each of the following sequences? 1 , 3 , 3 2 , 3 3 ,
ID: 3216209 • Letter: H
Question
How many terms are there in each of the following sequences? 1 , 3 , 3 2 , 3 3 , … , 3 99 1 , 3 , 3 2 , 3 3 , … , 3 99 9 , 13 , 17 , 21 , 25 , … , 353 9 , 13 , 17 , 21 , 25 , … , 353 38 , 39 , 40 , 41 , … , 238 38 , 39 , 40 , 41 , … , 238 (Billstein 33)Billstein, Rick. Problem Solving Approach to Mathematics for Elementary School Teachers, A, 12th Edition. Pearson, 20160401. VitalBook file.
How many terms are there in each of the following sequences? 1 , 3 , 3 2 , 3 3 , … , 3 99 1 , 3 , 3 2 , 3 3 , … , 3 99 9 , 13 , 17 , 21 , 25 , … , 353 9 , 13 , 17 , 21 , 25 , … , 353 38 , 39 , 40 , 41 , … , 238 38 , 39 , 40 , 41 , … , 238 (Billstein 33)
Billstein, Rick. Problem Solving Approach to Mathematics for Elementary School Teachers, A, 12th Edition. Pearson, 20160401. VitalBook file.
How many terms are there in each of the following sequences? 1 , 3 , 3 2 , 3 3 , … , 3 99 1 , 3 , 3 2 , 3 3 , … , 3 99 9 , 13 , 17 , 21 , 25 , … , 353 9 , 13 , 17 , 21 , 25 , … , 353 38 , 39 , 40 , 41 , … , 238 38 , 39 , 40 , 41 , … , 238 (Billstein 33)
Billstein, Rick. Problem Solving Approach to Mathematics for Elementary School Teachers, A, 12th Edition. Pearson, 20160401. VitalBook file.
Explanation / Answer
The question is very poorly typed. It is very difficult to make out what the question asks.
The first series is:
1, 3, 32, 33 ...... 399.
This is a geometric series.
This can be written as
30, 31, 32, 33 ...... 399.
As the powers of 3 go from 0 to 99, there are 0 + 99 + 1 = 100 terms.
The second series is
9, 13, 17, 21, 25.....353.
This is an arithmetic series with first term a = 9 and common difference d = 13 - 9 = 17 - 13 = 21 - 17 = 25 - 21 = 4.
The last term is 353.
The nth term formula is a + (n - 1) d.
The nth term is 353 => 9 + (n - 1) * 4 = 353
=> 9 + 4n - 4 = 353
=> 4n = 353 - 9 + 4
=> 4n = 348
=> n = 348/4
=> n = 87.
There are 87 terms in the series.
The last series is
38, 39, 40, 41 ....238.
This is also an arithmetic series with first term a = 38 and common difference d = 1.
The nth term is 238 => a + (n - 1) d = 238
=> 38 + (n - 1) * 1 = 238
=> 38 + n - 1 = 238
=> n = 238 - 38 + 1
=> n = 201
There are 201 terms in the series.
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