Question

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

Answer 1

5, 7, 9, 11, 13,…

S_n = 480

a = 5, d = 2, S_n = 480

S_n = `"n"/2 (2"a" + ("n" - 1)"d")`

480 = `"n"/2 [2 xx 5 + ("n" - 1)2]`

= `"n"/2[10 + 2"n" - 2]`

480 = `"n"/2[8 + 2"n"]`

8n + 2n² = 960

2n² + 8n – 960 = 0

⇒ n² + 4n – 480 = 0

⇒ n² + 24n – 20n – 480 = 0

⇒ n(n + 24) – 20(n + 24) = 0

⇒ (n – 20)(n + 24) = 0

⇒ n = 20, – 24

No. of terms cannot be negative.

∴ No. of consecutive odd integers beginning with 5 will sum to 480 is 20.