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How do you answer this arithmetic progression question?

If a boy saved P(Peso)25 on the first day,P27 the second day,P29 the third day,and,so on, How many days will it take him to save P880?

Sagot :

Mlcparra16idn
This is the formula for the sum of an arithmetic series
[tex] \frac{n}{2} [2 a_{1} +(n-1)d][/tex] (d is for the difference and n is for the number of terms)
We substitute  the values
[tex] \frac{n}{2} [50+(n-1)2] = 880 [/tex]
[tex] \frac{n}{2} [50+2n-2] [/tex]
[tex] \frac{n}{2} [48+2n][/tex]

[tex]1760=n[48+2n][/tex]
[tex]1760=48n+ 2n^{2} [/tex]
[tex]0=48+ 2n^{2} -1760[/tex]
[tex]0=(2n+88)(n-20) [/tex]

[tex]2n+88=0 [/tex]
[tex]2n=-88[/tex]
[tex]n=-44[/tex]
which is not possible

[tex]n-20=0[/tex]
[tex]n=20[/tex]

Therefore it will take 20 days