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What is the answer for finding the sum of the arithmetic sequence with a sigma notation with a 25 on top and t1 on the bottom then 5t-3 on the rightside?
Wiki User
∙ 15y ago
To find the sum of 25 terms of these arithmetic sequence you can use the formula:
Sn = (n/2)(a1 + an), where n is the number of terms in the sequence, a1 is the first term, and an is the last term of the sequence. In our case n = 25, so we need to compute a1 and a25.
Since an = 5t - 3, then
a1 = 5(1) - 3 = 5 - 3 = 2
a25 = 5(25) - 3 = 125 - 3 = 122
By substituting the values we know into the formula we have:
S25 = (25/2)(2 + 122) = (25/2)(124) = 25 x 62 = 1,550
Or you can use the formula:
Sn = (n/2)[2a1 + (n - 1)d] where d is the common difference.
In order to find d, we need to find at least the value of 2 terms and subtract them.
a1 = 2
a2 = 5(2) - 3 = 10 - 3 = 7
So d = 7 - 2 = 5
By substituting the values we know into the formula we have:
S25 = (25/2)[2(2) + (25 - 1)5]
S25 = (25/2)(4+ 120) = (25/2)(124 = 25 x 62 = 1,550
Thus, the sum of 25 terms of the given arithmetic sequence is 1,550.
Wiki User
∙ 15y ago
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