CAT 2024 - Slot 1 Quant Question 4

Using the arithmetic progression formula for the nth term, where
x_n = a + (n – 1) d
Substituting the value for n and using that in the equation that is given,
2x₆ + 2x₉ = x₁₁ + x₁₃
Then, x₁₀₀ equals
We get, 2(a + 5d) + 2(a + 8d) = a + 10d + a + 12d
4a + 26d = 2a + 22d
2a = – 4d
a = – 2d
We are given, x₅ = – 4
a + 4d = – 4
Substituting the value for a in terms of d,
2d = – 4
d = – 2
a = 4
x₁₀₀ = a + 99d
x₁₀₀ = 4 – 198 = – 194