Question

Find n and a_n where a=2, d=8 ,S_{n =90}

Answer 1

S_n = n/2 [2a + (n -1)d]

90 = n/2 [4 + (n -1)8]

180 = n[4+8n -8]

180 = n[8n -4]

180 = 8n² -4n

8n² - 4n - 180 =0

2n² - n - 45 =0

2n² - 10n + 9n -45 =0

(n -5) (2n+9) =0

SO n = 5

a_n = a + (n -1)d

= 2 + (5 -1)8

= 2 + 32 = 34