How many terms of the A. P 24,20, 16,must be taken so that the summay

1.	How many terms of the A. P 24,20, 16,must be taken so that the summay be 72? Explain the double answer.
Answer» first term =24 , common difference = --4 Sn = n / 2 { 2a + (n-1)d } = 72 n / 2 { 2 x24 + (n - 1) x-4} = 72 n { 48 -4n +4 } = 72x2 = 144 n(52 - 4n } = 144 ===> 4n^2 - 52n + 144 = 0 n^2 - 13n +36 = 0 ===> n = -9 , -4 { number of terms should be positive so n = 9 , 4} no of terms is equal to 9 & 4

How many terms of the A. P 24,20, 16,must be taken so that the summay be 72? Explain the double answer.

Answer»

first term =24 , common difference = --4

Sn = n / 2 { 2a + (n-1)d } = 72

n / 2 { 2 x24 + (n - 1) x-4} = 72

n { 48 -4n +4 } = 72x2 = 144

n(52 - 4n } = 144 ===> 4n^2 - 52n + 144 = 0

n^2 - 13n +36 = 0 ===> n = -9 , -4 { number of terms should be positive so n = 9 , 4}

no of terms is equal to 9 & 4