2. What is the 25th term of the sequence 3, 6, 11, 18, … ?
Look at the differences: 3,5,7,...
So the terms are
3, 3+3, 3+3+5, 3+3+5+7, ...
The sum 1+3+5+... = n^2
so, 3+3+5+7+... = n^2+2
The 25th term is 25^2 + 2 = 627
Hloniphile
To find the 25th term of the sequence, we need to determine the pattern first.
Looking at the sequence, we can see that each term is obtained by adding a consecutive odd number:
3 + 3 = 6, 6 + 5 = 11, 11 + 7 = 18, and so on.
So, the pattern is as follows:
3, 6, 11, 18, 27, 38, ...
Now we can determine the 25th term:
To find the 25th term, we need to find the sum of the first 24 terms plus the initial term (3).
Using the formula for the sum of an arithmetic sequence:
Sn = n/2 * (first term + last term), where n is the number of terms.
Plugging in the values:
S24 = 24/2 * (3 + last term)
Since we know that the 24th term is 38 (from observing the pattern), we can substitute it in:
S24 = 24/2 * (3 + 38)
S24 = 12 * 41
S24 = 492
Now, we can find the 25th term by adding this sum to the initial term:
25th term = 492 + 3
25th term = 495
Therefore, the 25th term of the sequence 3, 6, 11, 18, ... is 495.
To find the 25th term of the sequence, we first need to identify the pattern in the given sequence.
Looking at the sequence 3, 6, 11, 18, ... we can observe that each term is obtained by adding a certain number to the previous term.
The difference between consecutive terms is increasing by 2 each time:
6 - 3 = 3,
11 - 6 = 5,
18 - 11 = 7.
So, the difference between the 25th term and the 24th term would be (24th term difference) + (2 * number of steps from 24th term to 25th term).
To find the 24th term difference, we can subtract the 24th term from the 23rd term:
18 - 11 = 7.
Now, since we need to find the 25th term, we need to take the 24th term and add the difference between consecutive terms 25 - 24 times.
The 24th term is 18, and the difference between consecutive terms is 7. Adding this difference 25 - 24 times gives us:
18 + (7 * 1) = 18 + 7 = 25.
So, the 25th term of the sequence is 25.