Question

23. The sum of a certain number of terms of an AP series 8, 6, 4,.
is 52. The number of
​

Answer 1

Answer:

The sum of a certain number of terms of an AP series 8, 6, 4,.

is 52. The number of

Step-by-step explanation:

Let the number of terms is N.

Given,

First term ( a ) = -8

Common difference ( d ) = Difference of two consecutive terms

                               = ( -6 ) - ( -8 ) = -6 + 8 = 2.

Now,

⇒ Sum of  N terms of an A.P. = N/2 { 2 a + ( N - 1 ) d }

⇒ 52 = N/2 { 2 × ( -8 ) + ( N - 1 )2 }

⇒ 52 = N/2 { -16 + 2N - 2 }

⇒ 52 = N/2 ( -18 + 2N )

⇒ 52 × 2 = N ( -18 + 2N )

⇒ 104 = -18N + 2N²

⇒ 104 = 2 ( -9N + N² )

⇒ 104/2 = -9N + N²

⇒ 52 = -9N + N²

⇒ 0 = N² - 9N - 52

⇒ 0 = N² - 13N + 4N - 52

⇒ 0 = N ( N - 13 ) + 4 ( N - 13 )

⇒ 0 = ( N - 13 ) ( N + 4 )

∴ N = either 13 or -4.

But the numbers of terms in an A.P. can't be negative.

Therefore, the possible value is 13.