Arithmetic sequences

Question

Find the second term of the arithmetic series having the given data.

d=-3, n=12, S_n=-114

a₁=13, a_n=-20, S_n=150

 

Please show me the formulas and the steps you take to solve this problem.

Answer 1

S_n = (n/2)(2a₁ + (n - 1)d)

-114 = (12/2)(2a₁ + 11(3)) - Solve for a₁ and answer

 

S_n = (n/2)(a₁ + a_n)

150 = (n/2)(13 + (-20)) - Solve for n, then

a_n = a₁ + (n - 1)d

-20 = 13 + 19d - Solve for d and answer