Question

Mylo wishes to buy a cellphone worth Php8,000 six weeks from now. He starts saving Php100 the first week, Php200 the second week, Php400 the third week and so on. Will he be able to buy the cellphone after 6 weeks? Justify your answer.

Answer 1

No, he won't

Explanation:

Model it with a geometric sequence:
`a_n= 100(2)^(n-1)`

Now at first I interpreted the question as the total amount saved by the end of week being listed above, but if he saves the amount listed above each week and adds it to his total savings then:

`S_6= 100*((1-(2)^6)/(1-2))=6300`

He will only have `6300`PHP after 6 weeks, so unfortunately he won't be able to buy the phone.