The first term in a sequence is 1 and the second term is 5. From the

Question

The first term in a sequence is 1 and the second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence?

A. 2.5 
B. 3 
C. 5 
D. 25 
E. 50

HungNguyen · Answer

The average of 2 first term will always be the next term begin from the 3th term

=> average of 1 and 5 is (1+5)/2 = 3
=> the next term will always be 3 => 25th term will be 3 
=>answer is B (3)

Let's try another number:
let the first 2 term is 3 and 7 (because the last first 2 term was 1 and 5 , 1 and 5 are odd numbers , 5-1 = 4) = > 3 and 7 are odd numbers and 7-3 = 4

=> the average of 3 and 7 is (3+7)/2 = 5
=> the next term will always be 5 
=> the 3th term will equal (3+7+5)/3 = 15/3 = 5

chetan2u · Answer

Hi
First term = 1...
second term = 5..
third term =  \frac{(1+5)}{2} = 3 ...
Now we should realize that average of 3 terms is 3.. it will remain 3 for rest of the term..
fourth term = \frac{(1+5+3)}{3} = \frac{9}{3} = 3 ..
fifth term =  \frac{(1+5+3+3)}{4} =\frac{12}{4} = 3

ans  25th = 3 
B

Divyadisha · Answer

The answer is 'B'

1st Term= 1
2nd term= 5
3rd term= 6/2=3
4th term=1+5+3/3= 3

'3' is a repeating number after 3rd term

CrackverbalGMAT · Answer

Questions on sequences are mostly designed to give you a fright by asking you to find what seems like a humongous value. However, in all such questions on sequences, remember that however big the number you are trying to find out, if you are able to decipher a pattern, you are just a few steps away from the answer.

IN this question, the first term  t_1  = 1 and the second term  t_2  = 5.

The average of these two terms =  \frac{1 + 5}{2}  = 3.

Now, the question says that, from the third term onwards, each term is the average of all preceding terms.

Therefore, the third term  t_3  = 3. This is equivalent to adding three to the sum in each consecutive step. This means that the average of all the preceding terms will always be 3, regardless of the number of terms.

For example, the fourth term  t_4  =  \frac{1 + 5 + 3}{3}  =  \frac{9}{3}  = 3.

The fifth term  t_5  =  \frac{1 + 5 + 3 + 3}{4}  =  \frac{12}{4}  = 3.

We can now conclude that, if we proceed in this manner, each term from the 3rd term onwards will be 3. So, the 25th term,  t_{25}  = 3. 
The correct answer option is B.

Hope this helps!

SIDDHARTH1901 · Answer

First term = 1
second term = 5
third term = (1+5)/2=3
Forth term = (1+5+3)/3 = 3
Fifth term = (1+5+3+3)/4 =3
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.
.
.
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25th term = 3

ans 
B

Posted from my mobile device

MathRevolution · Answer

First-term:  1

Second term:  5

Third term:  \frac{1 + 5 }{ 2} = 3

Fourth term:  \frac{1+ 5 + 3 }{ 3} = 3

Fifth term:  \frac{1 + 5 + 3 + 3 }{ 4} = 3

Sequence: 1, 2, 3, 3, 3, 3, 3 ....

25^{th} term = 3

Answer B

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