teraslintu wrote:a) Write an expression for Sn, for the series 1 + 7 + 13 + ...
b) Hence, find the value of n for which Sn=833
Please help me.... I don't even know where to begin.
You are asking us to
guess what you mean!
My first thought was that just three terms is not enough to identify a sequence. Here it happens that 7= 1+ 6 and 13= 7+ 6 so we can
guess that this is an arithmetic sequence with initial value of 1 and common difference 6. But you understand, I hope, that there are infinitely many different sequences that start "1, 7, 13, …". Also, while [tex]S_n[/tex] is commonly used for the "nth sum" it would have been better to actually say that!
Assuming this is an arithmetic sequence then we can write the nth term as [tex]a_n= 1+ 6(n-1)= 6n- 5[/tex] so that [tex]a_1= 6- 5= 1[/tex], [tex]a_2= 12- 5= 7[/tex], [tex]a_3= 18- 5= 13[/tex]. An arithmetic sequence has the nice property that the "average value" is equal to the average of the first and last terms. Here the first term is 1 and the nth term is, as I said above, [tex]6n- 5[/tex]. The average of those two numbers is (1+ 6n- 5)/2= 3n- 2 and that is the average of the entire n term sequence. So the sum is [tex]n(3n- 2)= 3n^2- 2n[/tex]. Again, you can check that for the three numbers given- if n= 1, that is 3- 2= 1, if n= 2, that is 12- 4= 8= 1+ 7, if n= 3, that is 27- 6= 21= 1+ 7+ 13. That sum will be 833 when [tex]3n^2- 2n= 833[/tex] or [tex]3n^2- 2n- 833= 0[/tex]. Solve that quadratic equation. (It has two roots but obviously we want the positive one.)