Question

Solve :25+22+19+........+x=115

Answer 1

U1 = a = 25

d = U2 - U1
d = 22 - 25
d = -3

Un = x
a + (n - 1) . d = x
25 + (n - 1) . (-3) = x
25 - 3n + 3 = x
x = 28 - 3n

Sn = 115
n/2 . (a + Un) = 115
n/2 . (25 + x) = 115
n/2 . (25 + 28 - 3n) = 115 (multiply with 2 for both sides)
n . (53 - 3n) = 230
53n - 3n² = 230
0 = 3n² - 53n + 230
0 = 3n² - 30n - 23n + 230
0 = 3n(n - 10) - 23(n - 10)
0 = (n - 10)(3n - 23)
n = 10 (acceptable)
n = 23/3 (not acceptable)

x = 28 - 3n
x = 28 - 3 × 10
x = 28 - 30
x = -2