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Question
How many consecutive odd integers beginning with 5 will sum to 480?
Solution
5, 7, 9, 11, 13,…
Sn = 480
a = 5, d = 2, Sn = 480
Sn = `"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.
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