Question

How many terms of the AP 3 , 5 , 7 , 9 .... Must be added to get the sum 120

Answer 1

Answer is 10

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Answer 2

Answer -

Given,

AP = 3, 5, 7, 9

d = 2

Sum of n terms, Sn = 120

$Sn = \frac{n}{2} [2a + (n - 1)d]$

$120 = \frac{n}{2} [2 \times 3 + (n - 1)2]$

$120 \times 2 = 6n + 2n(n - 1)$

$240 = 6n + {2n}^{2} - 2n$

$4n + {2n}^{2} - 240 = 0$

$2n + {n}^{2} - 120 = 0$

${n}^{2} + 12n - 10n - 120 = 0$

$n(n + 12) - 10(n + 12) = 0$

$(n + 12)(n - 10)$

$n = - 12 \: or \: n = 10$

Since n has two values and n = (-12) is negative therefore number of terms will be equal to 10.