Need Help In Maths Pleasse!!!!!!!!!!

[shadow67]

hey guys,

i need some help in maths grade 12. i hav an exam tomoro. what i dont understand is 'sequence and series'.

in this topic under geometric progression u know the one that contains ratios.

i know the formulae for n thterm nad the sum A(r^n - 1)

r - 1

what i dont know is that when we are finding the sum or nth termwhats the differnce between years and terms. some problems like this one:

 

a house costs on avergae $15000 in 1970 and increases in value by 10%every year. a man buys a house in 1970 then another one every year after that. how much money does he spend in total from 1970 to 1986.

 

now if we use the difference form 1986 to 1970 as ur 'n'. then the answer comes wrong becoz 'n' is in terms not years. so if u add i term more to that difference u get the right answer. so what i want to know is when to add a term and when to subtract a term when '''''years'''''' are given. PLEASE HELPPPPP!!!!!!!!!

[BrainForce]

Look! here...a=15000$ ...r=11/10...now..we have in a..r^0..thus in nth one we have r^n-1...therefore n=6 in ur expression...ur try is correct...

 

u can do this question by using growth & depreciation formula too...in that case..take n=16...answer will be---15000 x [11/10]^16...

[CraigD]

Posts #3 - 8 have been moved to 11533, because they were off-topic for the Science Projects and Homework forum.

[CraigD]

a house costs on avergae $15000 in 1970 and increases in value by 10%every year. a man buys a house in 1970 then another one every year after that. how much money does he spend in total from 1970 to 1986.

Sometimes it helps to visualize this sort of problem by writing data in table form, like this:

Year Cost of house

1974 15000.00

1975 16500.00 = 15000.00 * 1.1

1976 18150.00 = 16500.00 * 1.1 = (15000.00 * 1.1) * 1.1

1977 19965.00 = 18150.00 * 1.1 = ((15000.00 * 1.1) * 1.1 ) * 1.1

 

Notice that “increases by 10%” means “multiplied by 1.1”, and that ((15000.00 * 1.1) * 1.1 ) * 1.1 can be rewritten [math]15000.00 \cdot 1.1^3[/math]. With a bit of imagination, we can see that, for any year, the cost of a house will be [math]15000.00 \cdot 1.1^{\mbox{year}-1974}[/math]

 

For the problem in question, you could easily just calculate the value of each year’s house, add the 17 terms together, and have the answer. However, you’d be in trouble if the question were changed to “how much does he spend from 1970 to 3070”, or some other number too big for this approach.

 

For these problems, you’ll want to know (or, better yet, know how to derive) the formula for a geometric series. Shadow, you already appear to know it. With it, and the help of some tool that’ll either give logarithms or perform exponentiation (eg: a calculator or a sliderule), you can give an answer with just a few calculations, no mater what year is asked. If you’re not sure you’ve used it correctly, try using it, and comparing the result to what you get simply multiplying to get terms and adding them together, table-style.

what i dont know is that when we are finding the sum or nth termwhats the differnce between years and terms.

The terms in this series are the values of a house for each year. Had the problem said he was buying a house each month, they would be the value of a house for each month, etc.

 

Good luck, and post your results back here if you need them to be checked.