How many terms of the Arithmetic Progression 45, 39, 33

• Arithmetic Progression (C10)

How many terms of the Arithmetic Progression 45, 39, 33, ... must be taken so that their sum is 180 ? Explain the double answer.

Answer

S_n = 180

n/2 [90 + (n - 1)(-6)] = 180

90n – 6n² + 6n = 360

⇒ 6n² – 96n + 360 = 0

⇒ 6[(n – 6)(n – 10)] = 0

⇒ n = 6, n = 10

Sum of a₇, a₈, a₉, a₁₀ = 0

∴ n = 6 or n = 10