Question

How many terms of A.P. 18,15,12,... are needed to give the sum 45? Explain the double answer.

What is the explaination for the double answer?

Answer 1

The number of terms is "(3 or 10)".

Step-by-step explanation:

The AP is  18, 15, 12, .....

Here, first term(a) = 18 , common difference (d) = 15 - 18 = - 3

and sum($S_{n}$ = 45

∴ Sum($S_{n}$ = $\dfrac{n}{2}$ × {2a + (n - 1)d}

⇒ $\dfrac{n}{2}$ × {2 × 18 + (n - 1)(- 3)} = 45

⇒ 36 - 3n + 3 = 45 × 2 = 90

⇒ $n^{2}$ - 13n + 90 = 0

⇒ $n^{2}$ - 10n - 3n + 90 = 0

⇒ (n - 10)(n - 3) = 0

⇒ n = 10 or  3

∴ n = 3 or 10

Hence, the number of terms is "(3 or 10)".

Answer 2

Answer:

hence the answer is 3 (or) 10