SOLUTION: Determine the sum to 16 terms of the arithmetic series whose 7th term is 19 and whose 10th term is 25
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-> SOLUTION: Determine the sum to 16 terms of the arithmetic series whose 7th term is 19 and whose 10th term is 25
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You can put this solution on YOUR website! Since we are told that we have an arithmetic series, that means there is a common difference between terms. Call it "d".
So, first let's find what that common difference is.
We are told that the 7th term is 19
And that the 10th term is 25.
So we are adding the common difference to get from the 7th to 8th, 8th to 9th, 9th to 10th. Or a total of 3 times.
So 19 + 3d = 25
3d = 6
So d = 2.
Now let's find the 1st term. We are told that the 7th term is 19, so we add the common difference 6 times from the 1st term.
or A_1 + (7-1)*2 = 19
A_1 + 12 = 19
A_1 = 7
So we know the common difference =2, the first term is 7, and we know the number of terms we are adding.
We still need to know the last term. So the last term can be found by taking a_10 + (6-1)*2 = 25 + 10 = 35
The sum is:
number of terms*(1st term + last term)/2
16*(7+35)/2 =
