Find S25 for 1/2 + 1 + 3/2 + 2 +...
A. 160
B. 162
C. 160.5
D. 162.5
I think D
correct again,
looks like you have a handle on this topic
Is the answer 650
What is correct answer
To find S25, the sum of the first 25 terms of the given sequence, we need to determine the pattern and use the formula for the sum of an arithmetic series.
From the given sequence: 1/2, 1, 3/2, 2, ...
Looking at the terms, we can observe that each term is found by adding 1/2 to the previous term.
We can rewrite the sequence as follows:
1/2, 1/2 + 1, 1/2 + 1 + 1/2, 1/2 + 1 + 1/2 + 1, ...
The first term is 1/2 and the common difference is 1/2.
To find the sum of the first n terms of an arithmetic series, we use the formula:
Sn = n/2 * (a + l)
where Sn is the sum of the first n terms, a is the first term, l is the last term, and n is the number of terms.
In this case, n = 25,
a = 1/2,
l = the 25th term = a + (n-1) * d = 1/2 + (25-1) * (1/2) = 1/2 + 12 * (1/2) = 7/2.
Using the formula, we find:
S25 = 25/2 * (1/2 + 7/2) = 25/2 * 8/2 = 25/2 * 4 = 25 * 2 = 50.
Therefore, the sum of the first 25 terms of the given sequence is 50.
So, the correct answer is not given in the options provided.