In an arithmetic series t1 = 25, t3 = 23. Find the value of n for which Sn= 135

Question

There are two answers!

n=___?___

n=___?___

PLEASE HELP ME AND THANK YOU IF YOU DO!!!

Answer 1

Sum of an arithmetic series = n/2 * [(2t₁ + (n-1)*d]

t₁ = 25

d = (t3 - t1)/(3-1) = (25 - 23)/2 = 1

135 = n/2 * [2*25 + (n-1)*1]

135 = n/2 * [50 + n -1]

270 = n * [50+n-1]

270 = 50n + n² - n

0 = n² + 49n - 270

0 = (n-5) (n+54)

n=5

or n =-54