Question

how many terms of 3,5,9,9,........sum to 120​

Answer 1

Answer:

the term is not an ap 3 , 5 , 9 , 9

Answer 2

Given:-

• First term = a = 3
• Common difference = d = 5- 3 = 2
• Sum of terms = 120

To Find:-

• Number of terms = n = ?

Solution:-

$\sf \: S_{n} = \dfrac{n}{2} \{2a + (n - 1)d \} \\ \\ \sf \: 120 = \dfrac{n}{2} \{2(3) + (n - 1)2 \} \\ \\ \sf \: 240 = n (6 + 2n - 2) \\ \\ \sf \: 240 = 6n + 2n {}^{2} - 2n \\ \\ \sf \: 2n {}^{2} + 4n - 240 = 0 \\ \\ \sf \: n {}^{2} + 2n - 120 = 0 \\ \\ \sf \: n {}^{2} + 12n - 10n - 120 = 0 \\ \\ \sf \: n(n + 12) - 10(n + 12) = 0 \\ \\ \sf \: \boxed{ \bf \: n = 10} \: \: or \: \: \boxed{ \bf \: n = - 12}$

∴ n = 10 ✔

Because, n can't be equal to negative value(-12).

So, 10 terms would be sum up to 120.