Question

How many consecutive odd integers beginning with 5 will sum to 480

Answer 1

Answer:

475 is I think the answer

Answer 2

Answer:

20 Consecutive odd integers.  

Step-by-step explanation:

Series of Odd number form an AP.

So, the first term, a = 5

common difference, d = 2

Sum of n term, $S_n=480$

To find: Value of n.

We know that,

$S_n=\frac{n}{2}(2a+(n-1)d)$

$\frac{n}{2}(2\times5+(n-1)2)=480$

$n(10+2n-2)=480\times2$

$8n+2n^2=960$

$n^2+4n-480=0$

$n^2+24n-20n-480=0$

$n(n+24)-20(n+24)=0$

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

n = -24  and n = 20

Therefore, 20 Consecutive odd integers.