How many terms are there in the A.P. whose first and fifth terms are 14 and 2 respectively and the sum of the terms is 40?

Question

Philoid · Accepted Answer

a₅= a + (n -1) d

2 = -14 + 4d

16 = 4d

d = 4

S_n = [2a + (n – 1) d]

40 = [2(-14) + (n -1) (4)]

40 = 12n² – 16n

2n² – 16n -40 = 0

n² – 8n -20 = 0

n² – 10n + 2n – 20 = 0

(n – 10) (n + 2) = 0

n = 10 and n = -2 (not possible)