Question

How mamy terms of the series 5+7+9+..........must be taken in order that the sum may be 480

Answer 1

n=20 ,this answer may help you

Answer 2

The "number of terms (n) is 20".

Step-by-step explanation:

The given sequence are:

5 + 7 + 9 +.......... in AP.

Sum, $S_{n} =480$

Here, first term(a) = 5, common difference(d) = 7 - 5 = 2

To find, the number of terms(n) = ?

We know that,

The sum of nth term of an AP

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

⇒ $\dfrac{n}{2} [2\times 5+(n-1)2]=480$

⇒ $\dfrac{n}{2} (10+2n-2)=480$

⇒ $\dfrac{n}{2} (8+2n)=480$

⇒ $n^{2}+4n=480$

⇒ $n^{2}+4n-480=0$

⇒ $n^{2}+24n-20n-480=0$

⇒ $n(n+24)-20(n+24)=0$

⇒ $(n+24)(n-20)=0$

⇒ $n+24=0$ or $n-20=0$

⇒ n = 20 or - 24 [ n never is negative]

∴ n = 20

Hence, the "number of terms (n) is 20".