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it has to do with sequences..for example,

The first term of a sequence is -2, and each term after the first is obtained by multiplying the preceding term by 2, and adding 3. What is the 75th term of the sequence?

also

how would you find the sum of the first 75 terms, like if the question was like this:

The first term of a sequence is -2, and each term after the first is obtained by multiplying the preceding term by 2, and adding 3. What is the sum of the first 75 terms of the sequence?

also, what other type of questions would they ask on sequences, expect for these 2

thanks!

By User123 (User123) on Friday, October 08, 2004 - 02:16 pm: Edit

bump

By Legendofmax (Legendofmax) on Friday, October 08, 2004 - 02:27 pm: Edit

The formula is n(a+z)/2 where n is the number of items you have to add, a is the first and z is the last.

I don't know about the first one... seems messy.

By Madd87 (Madd87) on Friday, October 08, 2004 - 03:27 pm: Edit

Did you make the 1st question up? I really doubt that would be on the SAT since the answer is something insanely huge because of the exponential function you created..

if you want to know how to do it just write down the first like 6 or 7 terms and usually you will see a visible pattern. In this problem I did not, so I plugged the numbers into stat lists in my calculator, x list 1 , 2 , 3 ... and y list was the values +3 so they would all be positive.. then I found a exponential model which turned out to be 5.1165858e^(.6809x) -3 (-3 because I added 3 to all the terms)

this fits pretty well, but is not exact and if you subtitute 75 in for x you get something huge... 7.7 x10^21

I hope this helps although I dont see anything like it being on the SAT

By Slipstream99 (Slipstream99) on Friday, October 08, 2004 - 03:31 pm: Edit

To find the first one, you have to use the equation [2^(n-1)]-3. If you just write out the first 6 or 7 terms of the sequence (-2, -1, 1, 5, 13, 29, 61) you see that each sequence increases by 2 to the power of the number of the sequence minus 1. And, since it starts at -2, you have to subtract 3. So, the 75th term is [2^(74)]-3, which equals 1.888946593x(10^22).

By Jm2006 (Jm2006) on Friday, October 08, 2004 - 05:05 pm: Edit

Look for patterns

By Neelesh (Neelesh) on Friday, October 08, 2004 - 06:04 pm: Edit

yes i madde the question upformula..

thanks!

By Neelesh (Neelesh) on Friday, October 08, 2004 - 06:08 pm: Edit

but for the first one, is there like a fomula u can use for all those types of problems?

By Geniezclone (Geniezclone) on Saturday, October 09, 2004 - 07:00 am: Edit

there's no formula that gets you the sum of a sequence in which each term after the first is obtained by multiplying a number and THEN adding a number... that I know of... if there is, it'll be too complicated for you to use on the SAT... it'll be easier if you just list out the terms

there are only formulas for finding the sum of terms in an arithmetic sequence (as mentioned by Lengendofmax) and the sum of terms in a geometric sequence (in which each term equals the term preceding it multiplied by a number)