Question

How many terms of the ap 2,10,8 must be taken to give asum of 90

Answer 1

YouYour question needs a correction, AP is 2 , 10 , 18 ...

Answer:

5

Step-by-step explanation:

We know,

      Sum of n terms = ( n / 2 ){ 2a + ( n - 1 )d },         where a is the first term and d is the common difference between the terms.

Here, first term is 2 and common difference is 10 - 2 = 8

So, let the number of terms required be n.

⇒ 90 = ( n / 2 ){ 2( 2 ) + ( n - 1 )8 }

⇒ 90 x 2 = n{ 4 + ( n - 1 )8 }

⇒ 4 x 45 = 4n{ 1 + ( n - 1 )2 }

⇒ 45 = n( 1 + 2n - 2 )

⇒ 45 = n( 2n - 1 )

⇒ 45 = 2n^2 - n

⇒ 2n^2 - n - 45 = 0

⇒ 2n^2 - 10n + 9n - 45 =  0

⇒ 2n( n - 5 ) + 9( n - 5 ) = 0

⇒ ( n - 5 )( 2n + 9 ) = 0

⇒ n = 5 or 9 / 2

Hence the required number of terms is 5.