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Can someone explain 16, 17 and 18 to me? I did the rest of the review (as you can see on the top) but I just can’t understand these 3 questions

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Hi u/fifimushie,

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16a) The formula is directly telling you how to find the nth term in the series. So if you wanted to find the 2nd term plug in n=2, if you wanted to find the 3rd term, plug in n=3.  


16b, 17a, 17b) Its been a long time since I've done these types of problems, but I think there's formulas you should have been given for this . "Arithmetic" sum if the sequence is just adding/subtracting the same amount to get from one term to the next or "Geometric" sum if the sequence is multiplying/dividing by the same amount to get one one term to the next. Figure out the pattern, and you should be able to plug values into the appropriate formula.  
If you suspect its geometric, you can divide one term by the previous one to figure out what you would need to multiply by to get from one to the other, and then see if that pattern holds up.

18) You need the compound interest formula. Plug in all the given values and solve for the "principal" P (the starting amount)
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I tried read these over and over again but they don’t make sense in my brain. They’re patterns right? And I know that semi annually is twice a year but I’m just really confused and need help
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Looks like you are reviewing gr 11 math? And the last three questions are from the sequence and series chapter, which is often left till the end of the course because teachers see it as less important ( not necessary for gr 12 calculus).  

It is all formula based.  If the teacher hasn’t shown you, I would check out Khan Academy videos for arithmetic and geometric sequences and series.
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16b. Here is the formula for nth term of an arithmetic sequence that has same distance between terms. Suppose a1 means first term, d is the difference between neighboring terms, and n is the number of the term you seek.

terms: a1, a1+1d, a1+2d, a1+3d, ...

nth term: a1 + (n-1) * d

In this problem a1 is 12, n is 15, and d is the common difference you see between any two terms, such as 19 - 12.
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17a) The sum of the first n terms of an arithmetic sequence can be found using: the average of first term and nth term, multiplied by number of terms. (That's because a1 + a12 = a2 + a11 = a3 + a10 = ....)

(a1 + a12)/2 * 12

You know a1 is 32. You need to find a12, the twelfth term. Use the formula I gave in other comment for nth term of an arithmetic sequence. This one has a common difference of -3.

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