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?

1 Answer

Answer :

On the 20th day, you would reach 880. ---------------------------------------- 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.

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