SOLUTION: Find the number of terms of the sequence 1,4,7,10... Must be taken if the sum is to exceed 100.

Algebra ->  Human-and-algebraic-language -> SOLUTION: Find the number of terms of the sequence 1,4,7,10... Must be taken if the sum is to exceed 100.      Log On


   

Question 389888: Find the number of terms of the sequence 1,4,7,10... Must be taken if the sum is to exceed 100.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,        

Find the number of terms of the sequence 1,4,7,10... for s%5Bn%5D+%3E+100

S%5Bn%5D=%28n%2F2%29%282%2Aa%5B1%5D%2B+%28n-1%29d%29 In this example d = 3 and first term is = 1

    n/2 [2 + 3(n-1)] > 100

     n[2 + 3n-3)] > 200

     2n + 3n^2-3n > 200

    3n^2 - n - 200 = 0  n+=+%281+%2B-+sqrt%28+2401%29%29%2F%286%29=+%281%2B-49%29%2F6n=-8 or n= 8  1/3

S%5B9%5D=%284.5%29%282+%2B+%288%293%29=+117

  Nine terms must be taken for sum to be > 100