Secuencias aritmeticas

Question

In an arithmetic sequence the sum of the first  terms is given by

u1+⋯+un=Sn=n2−10n

Find u103.

Answer 1

I'm assuming that the equation ought to be S_n= n²-10n

If so, here's a hint to get you started in the right direction:

We know that S₁₀₃ = (103)²-10(103).

This would be u₁+u₂+ ... +u₁₀₃.

So to get the 103rd term, u₁₀₃, think about how you could go about subtracting the first 102 terms....

That should get you started!

Answer 2

S_n = n² - 10n, if so, then

S₁₀₃ = 103² - 10(103)