Question

How many terms of the AP , 9, 17 ,25 ... must be taken to give a sum of 636​

Answer 1

Answer:

AP - 9 , 17, 25 ,. .. .. .. .. .. ..

a = 9 a2 = 17

d = 17- 9

d= 8

S = 636

Step-by-step explanation:

S = n /2 ( 2a + (n -1)d)

636 = n/2 ( 2 ×9 + (n -1)8)

636 × 2 = n ( 18 + 8n - 8 )

1272 =n (10 +8n)

1272= 10n +8n^2.....Now you may solve it

Answer 2

Giver:-

• The AP , 9, 17 ,25 ...
• A sum of 636.

To find:-

• Find the nth term..?

Solutions:-

• Let the be n term of the Ap.

=> a = 9

=> d = a2 - a1 = 17 - 9 = 8

Sn = n/2 [2a + (n - 1)d]

=> 636 = n/2 [2 × 9 + (n - 1) 8]

=> 636 = n/2 [18 + 8n - 8]

=> 636 = n/2 [10 + 8n]

=> 636 = n/2 × 2 [5 + 4n]

=> 636 = n [5 + 4n]

=> 636 = 5n + 4n²

=> 4n² + 5n - 636 = 0

=> n² + 53n - 48n - 636 = 0

=> n(4n + 53) - 12(4n + 53) = 0

=> (n - 12) (4n + 53)

=> n - 12 = 0 or 4n + 53 = 0

=> n = 12 or n = -53/4

n is cannot be negative and fraction.

=> n = 12

Hence, the nth term of Ap is 12.