Question

How many terms of the series 5+7+9+⋯ must be taken so that sum may be 480? DONT WRITE ANYTHING IF YOU DONT KNOW!! HELP PLEASE

Answer 1

Answer:

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

Step-by-step explanation:

The given sequence are:

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

Sum, S_{n} =480S

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]S

n

=

2

n

[2a+(n−1)d]

⇒ \dfrac{n}{2} [2\times 5+(n-1)2]=480

2

n

[2×5+(n−1)2]=480

⇒ \dfrac{n}{2} (10+2n-2)=480

2

n

(10+2n−2)=480

⇒ \dfrac{n}{2} (8+2n)=480

2

n

(8+2n)=480

⇒ n^{2}+4n=480n

2

+4n=480

⇒ n^{2}+4n-480=0n

2

+4n−480=0

⇒ n^{2}+24n-20n-480=0n

2

+24n−20n−480=0

⇒ n(n+24)-20(n+24)=0n(n+24)−20(n+24)=0

⇒ (n+24)(n-20)=0(n+24)(n−20)=0

⇒ n+24=0n+24=0 or n-20=0n−20=0

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

∴ n = 20

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