Question

emman needs php 2520 for his baguio tour. He saves php 50 on his baon on the first week and ask for an additional php 20 from his tatay on the succeeding weeks. How many weeks does he need to request an additional to reach such amount? show solution in an arithmetic sequence.

Answer 1

Given :  Required 2520 . Saves 50 on 1st week and increase by 20 Each week

To Find : Number of weeks

Solution:

a = 50

d = 20

n =  ?

Sₙ = 2520

Sₙ  = (n/2)(2a + (n-1)d)

=> (n/2)(2*50 + (n-1)(20)) = 2520

=> n ( 100 + 20n - 20)  = 5040

=> n(20n + 80) = 5040

=> n(n + 4) 20 = 5040

=> n(n + 4)  = 252

=> n² + 4n - 252 = 0

=> n² + 18n -14n - 252 = 0

=> n(n +18) - 14(n + 18)  = 0

=> (n - 14)(n + 18) = 0

=> n = 14

14 Weeks

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