Question

In the sum of n successive odd numbers starting from 3 is 48 , find the value of n.

Answer 1

Ans :- n=6

Solu:-

By using A.P formula

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

a = 3, d = 2 (sucessive odd number difference )
Sum= 48

48 = (n/2)*[2(3)+(n-1)*2]
48 = n*[3+n-1]
${n}^{2} + 2n - 48 = 0$
${n}^{2} + 8n - 6n - 48 = 0$
$n(n + 8) - 6(n + 8) = 0$
$(n - 6)(n + 8) = 0$
$n = 6 \: or \: - 8$
$n > 0$
so n=6