Math problem?!? Help ASAP?
Find S(n) for the indicated series.
S(18) for 5+8+11+...
My teachers answer key said the answer was 549. I on the other hand got 56. I really dont understand how she got that answer. Please help!
Find S(n) for the indicated series.
S(18) for 5+8+11+...
My teachers answer key said the answer was 549. I on the other hand got 56. I really dont understand how she got that answer. Please help!
Comments
You found t(18). The 18th term. However, this question is asking for S(18), which is the sum of all the terms.
S(18) = 5 + 8 + 11 + ... + 56
S(18) = SUM [x = 1 -> 18] 3x + 2
S(18) = 3(18)(19)/2 + 2(18)
S(18) = 549
You need to sum the first 18 terms in the series(That's what the S(18) means). Note that in this case, this is an arithmetic series, so the sum would actually be:
Sum = (Total terms)/2 *(First term + 18th term)
= (18)/2 * (5 + 3(18) + 2) = 9 * (7 + 54) = 549
Note that I got the 18th term from the fact that the nth term in an arithmetic series can be written as:
a_n = dn + c where d is the common difference among terms and c is the first term minus common difference.
a_n = 3n + 2
So a_18 = 3(18) + 2 = 56
Ok well it is because you found a sub n. The objective was to find the summation. So the formula for the summation is S sub n=n*(a sub 1+a sub n/2(. So it would be S sub 18=18*(5+56/2) which would equal S sub 18=18*(61/2). Solve that and S sub 18 would equal 549.