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What Sum of the terms of Arithmetic Progression If a boy saved 25 on the first day 27 on the second day 29 the third day and so on how many days it will take him to save 880?
Wiki User
∙ 6y ago
On the 20th day, you would reach 880.
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Sum(AP) = ½n(2a + (n-1)d)
here:
Sum(AP) = 880
a (first term) = 25
d (common difference) = 2
n (number of terms) = unknown
Plugging in the values gives:
880 = ½n(2×25 + (n - 1) × 2)
→ 880 = n(25 + n - 1)
→ 880 = 24n + n²
→ n² + 24n - 880 = 0
→ (n - 20)(n + 44) = 0
→ n = 20 or -44
You cannot have -44 days, so it must be on the 20th day when he puts 25 + (20 - 1)* 2 = 63 in that he reaches a total of 880.
The sum of an AP can also be expressed as ½ × n × (first + last) since last = first + (n - 1) × difference.
Wiki User
∙ 6y ago
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