<p>each term is 2 less than the previous term. if the third term of this sequence is 1. what is the first term?
i know how to solve it but in a timeconsuming way
so i want the best shortcut answer :)</p>
<p>1+2*2=5
Best way I could think of</p>
<p>5, 3, 1
10 char</p>
<p>tn=a+(n-1)d
1=a+(-2)*2
or,1=a-4
a=5
Doing this in your brain wont take just few seconds</p>
<p>If you want the best way (that is, doing work that guarantees that an answer is correct),</p>
<p>The first term is x
Second term: x-2
Third term: (x-2) - 2</p>
<p>And we know that the third term equals 1, so solve for x.
(x-2) - 2 = 1
x - 2 = 3
x = 5</p>
<p>So, the first term is 5.</p>
<p>If you are really good at these types of problems, that do some backtracking: 1+2 = second term, 1+2+2 = first term</p>
<p>oooops i wrote the question wrong…reaaly sooorrry 
all these ways shown could be for such easy question but it would be time consuming for this question below
it should be :
each term is 2 less than the square root of the previous term. if the third term of this sequence is 1. what is the sixth term?</p>
<p>Is this a SAT II math question??? because there isn’t imaginary numbers in SAT</p>
<p>IF you backtrack, the 1st term should be 121, second term is 9, third term is 1, 4th term is -1, 5th term is -2+i, 6th term is sqrt(-2+i) - 2</p>
<p>Not sure if that’s the answer…</p>
<p>1 + 4 = 5 </p>
<p>Nobel Prize Please?</p>
<p>@eagle4022 why are you finding the first and second terms?</p>
<p>1, -1, -2+i, sqrt(-2+i) - 2. Convert -2+i to polar, take the square root, convert the answer back to rectangular form.</p>