SOLUTION: The sum of the first n terms of a series is 5n^2-2n. The r-th term is... a) 6r+3 b) 10r-7 c) 4r^2-r d) r(5r-2) e)3r

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Question 1123342: The sum of the first n terms of a series is 5n^2-2n. The r-th term is...
a) 6r+3 b) 10r-7 c) 4r^2-r d) r(5r-2) e)3r
Found 2 solutions by ikleyn, incline dybala:
Answer by ikleyn(52790) About Me  (Show Source):
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The sum of the first n terms of a series is 5n^2-2n. The r’th term is...
a) 6r+3 b) 10r-7 c) 4r^2-r d) r(5r-2) e)3r
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The r-th term is the difference between the first r terms and the sum of the first (n-1) terms, i.e.


a%5Br%5D = (5*r^2-2*r) - (5*(r-1)^2-2*(r-1)) = 


           = 5r^2 - 2r - 5r^2 + 10r - 5 + 2r - 2 = 10r - 7.


Answer.  10r - 7.  Options b).


Answer by incline dybala(1) About Me  (Show Source):
You can put this solution on YOUR website!
.

The r-th term is the difference between the first r terms and the sum of the first (r-1) terms, i.e.

a[r] = (5*r^2-2*r) - (5*(r-1)^2-2*(r-1)) =

= 5r^2 - 2r - 5r^2 + 10r - 5 + 2r - 2 = 10r - 7.

Answer. 10r - 7. Options b).

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