What is the sum of series of arithmetic progression having a common difference of 3.5, if the first term is 0.5 and the last term is 25?
Question
Solution
The sum of an arithmetic series can be found using the formula:
S = n/2 * (a + l)
where: S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
First, we need to find the number of terms (n). We can use the formula for the nth term of an arithmetic sequence:
a + (n - 1) * d = l
where: a is the first term, d is the common difference, and l is the last term.
Substituting the given values:
0.5 + (n - 1) * 3.5 = 25
Solving for n gives:
n = (25 - 0.5) / 3.5 + 1 n = 7
Now we can find the sum of the series:
S = 7/2 * (0.5 + 25) S = 3.5 * 25.5 S = 89.25
So, the sum of the series is 89.25.
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