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

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

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

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!

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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