Answer:
Sn = n^2+4n, and n = 11
Step-by-step explanation:
Sorry that i'm late, but i think i see what you did wrong here;
What you entered in as that Sₙ = 2n + 3, but instead the nth term (aₙ) was equal to 2n + 3. How? Well you know the following formula;
aₙ = a₁ + (n-1)d
here the difference = 2 & a₁ = 5
aₙ = 5 + 2(n-1) = 5 + 2n - 2 = 2n + 3
So the aₙ = 2n + 3, not Sₙ. The sum of the series would be calculated using the following formula:
Sₙ = n/2[2a₁ + d(n-1)]
= n/2[2(5) + 2(n-1)] = n^2+4n
Now then we have to determine n where the series sum is 165. Let's plug in this value;
165 = n^2 +4n,
n = 11 & n = -15
n has to equal 11 here
(I hope this helps future students)
