SOLUTION: The Question: "The nth term of a series is {{{ (1/2)(2n-1) }}}. Write down the (n+1)th term. a) prove that the series is an arithmetic progression. b) find, algebraically,

Algebra ->  Sequences-and-series -> SOLUTION: The Question: "The nth term of a series is {{{ (1/2)(2n-1) }}}. Write down the (n+1)th term. a) prove that the series is an arithmetic progression. b) find, algebraically,      Log On


   

Question 922010: The Question:
"The nth term of a series is +%281%2F2%29%282n-1%29+. Write down the (n+1)th term.
a) prove that the series is an arithmetic progression.
b) find, algebraically, the value for n for which the sum to n terms is 200"


-I have written the (n+1)th term +%281%2F2%29%282n%2B1%29+
-I have also done part a) of the question by subtracting the nth term from the (n+1)th term to find that the common difference between the terms is 1.
-I also know that the formula for an arithmetic progression is +Un=a%2B%28n-1%29d+
please help with part b) of the question
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
"The nth term of a series is +%281%2F2%29%282n-1%29+. Write down the (n+1)th term.
a) prove that the series is an arithmetic progression.
b) find, algebraically, the value for n for which the sum to n terms is 200"
S(n) = n(a(1)+a(n))/2
200 = n((1/2)+(1/2)(2n-1))/2
400 = n((1/2)(1+2n-1)
400 = n*n
n = 20
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Cheers,
Stan H.
----------------
-I have written the (n+1)th term +%281%2F2%29%282n%2B1%29+
-I have also done part a) of the question by subtracting the nth term from the (n+1)th term to find that the common difference between the terms is 1.
-I also know that the formula for an arithmetic progression is +Un=a%2B%28n-1%29d+
please help with part b) of the question