Need to check for this question:
25. The sum of the first six terms of an arithmetic sequence is -12 and the sum of it's first fourteen term is 196. Find (a) in the sum of n terms, (b) the smallest value of n if the sum is to exceed 250.
I got the part a fine by using the formula Sn = (n/2)[2a + (n-1)d] and simultaneous equations, but the answer I got was 2n^2 - 12n....and the answer at the back is 2n^2 - 14n.
In part b I'm having trouble following. I tried using quadradics but with either one I end up getting surds (which is probably the point since 250 isn't a factor that fits nicely with either of them). And I don't think it possible to do logs because there are three terms...
If anyone could help that would be much appreciated, thanks ^^
Hey! Just setting n=6, you'll see that the only equation that gets out the required value of -12 is the one at the back of the book. Potentially you messed up some algebra somewhere? Check it over, and if you still need help, post it here and I'll take a look!
As for the second part, you're 100% on the right track. Set your equation equal to 250, and find the surd value. Using the equation at the back of the book, n will equal -8.215 and 15.215. Now, obviously n can't be zero, so we take the positive value 15.215. Let's think about what that means for a second; if n=15, the answer will be LESS than 250. If n=16, the answer will be MORE than 250. So, 16 is out answer, because that's what the question wants!
Let me know if that all makes sense.
Jake