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?

Answer 1

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.