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Justice Nichols
Mathematics
23 January, 08:38
Find the sum of the first 25 terms. 2,8,14,20
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Lorelai Ross
23 January, 08:45
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This is an arithmetic sequence as each term has a common difference to the previous term. Any arithmetic sequence can be expressed as:
a (n) = a+d (n-1), a=initial term, d=common difference, n=term number.
We know that a=2 and d = (20-14) = (14-8) = (8-2) = 6 so
a (25) = 2+6 (25-1)
a (25) = 146
The sum of an arithmetic sequence is the average of the first and last terms times the number of terms, in this case:
s (25) = 25 (2+146) / 2
s (25) = 1850
And if you care to remember the arithmetic sum formula it is:
s (n) = (2an+dn^2-dn) / 2, using a=2, d=6, and n=25 we get:
s (25) = (4 (25) + 6 (25^2) - 6 (25)) / 2
s (25) = 1850
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