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Sally had P3.00 on August 1 and was determined to add to this every day. She had P3.25 on August 2; P3.50 on August 3; and P3.75 on August 4 and so on until August 31. How much would she have at the end of August?

Sagot :

This is an Arithmetic sequence.

An arithmetic sequence is shown as:
[tex]a_1,a_2,a_3,...,a_n[/tex]
and 
[tex]a_2-a_1=a_3-a_2=...=a_n-a_{n-1}=d[/tex]

We don't know [tex]a_n[/tex] which  is the last term and it is computed by:
[tex]a_n=a_1+d(n-1)[/tex] 

Our [tex]a_1[/tex] is the amount Sally had on August 1 which is equal to 3.00
We compute for [tex]a_n [/tex] which is also [tex]a_{31}[/tex]. The common difference in the problem is 0.25.

[tex]a_{31}=3.00+0.25(31-1)=3.00+0.25(30)=3.00+7.50=10.50[/tex]

Therefore she would have P10.50 by the end of August.