Sorry about the failed question before, the sigma notation proved difficult to transfer accurately. Never the less, here is another similar question- once I solve this I will be able to do the other one.
We are given conditions for a sequence / series in sigma notation;
The rule that n follows = Un
The last value that n has = N
The first value n has = 1
We are given these conditions and told it = 2200; we have to find the value of N
So I tried using the formal Sn = 1/2n (a + L )
a=1, as the rule is Un and the first value of n=1
L=N (as we are told this in the question
2200 = 1/2N (1 + N)
4400 = N + N²
N² + N – 4400 = 0
a=1 b=1 c=-4400
b² - 4ac = 1² - (4 * 1 * -4400) =17601
N = (-)1 +/- √17601 / 2 = 65.834 (ignore 1- as cannot have a negative number of terms)
My issue is N cannot be a decimal- you cannot have .834 of a term so where am I going wrong?
Cheers.
We are given conditions for a sequence / series in sigma notation;
The rule that n follows = Un
The last value that n has = N
The first value n has = 1
We are given these conditions and told it = 2200; we have to find the value of N
So I tried using the formal Sn = 1/2n (a + L )
a=1, as the rule is Un and the first value of n=1
L=N (as we are told this in the question
2200 = 1/2N (1 + N)
4400 = N + N²
N² + N – 4400 = 0
a=1 b=1 c=-4400
b² - 4ac = 1² - (4 * 1 * -4400) =17601
N = (-)1 +/- √17601 / 2 = 65.834 (ignore 1- as cannot have a negative number of terms)
My issue is N cannot be a decimal- you cannot have .834 of a term so where am I going wrong?
Cheers.