Question

Class 10



How many terms of the AP : 9,17,25....

must be taken to give a sum of 636?


Answer - 12​

​

Answer 1

Answer:

12

Step-by-step explanation:

AP : 9, 17, 25,......

Here, the given data is as follows -

a = 9,

Common difference (d) = 17 - 9 = 8

Sₙ = 636

We need to find the number of terms(n).

We will use the following formula -

Sₙ = $\sf \frac{n}{2}$ [2a + ( n - 1 ) d ]

⇒ 636 = $\sf \frac{n}{2}$ [ 2 * 9 + ( n - 1 ) 8 ]

⇒ 636 * 2 = n [ 18 + 8n - 8 ]

⇒ 1272 = n [ 10 + 8n ]

⇒ 1272 = 10n + 8n²

⇒ 8n² + 10n - 1272 = 0

⇒ 2 ( 4n² + 5n - 636 ) = 0

⇒ 4n² + 5n - 636 = 0

We got a quadratic equation here, let's solve it ;

⇒ 4n² + 5n - 636 = 0

⇒ 4n² + 53n - 48n - 636 = 0

⇒ 4n ( n - 12 ) + 53 ( n - 12 ) = 0

⇒ ( n - 12 ) ( 4n - 53 ) = 0

⇒ n = 12 or n = $\sf \frac{-53}{4}$

Out of these two roots, only one root i.e., n = 12 is admissible.

Hence, the required number of terms is 12.