<p>The first term of the sequence above is 2, and every term after the first term is -2 times the preceding term. How many of the first 50 terms of this sequence are less than 100?</p>
<p>A) 22
B) 25
C) 28
D) 30
E) 37</p>
<p>The answer is C, I sadly cannot get the book's answer. Please explain to moi! Por favor!! :D</p>
<p>so half of the number must be under 100, because they are negative. The other 3 are 2, 8,32.</p>
<p>To start off right down the beginning of the sequence:</p>
<p>2, -4, 8, -16, 32, -64, and so on</p>
<p>Hopefully you can figure out how i got that part of the sequence ( -2 times the preceding term, so -2 times 2 gives me -4, and -4 times -2 gives me 8 and so forth). Anyhow from that how many terms are less than 100? The answer to that would be 6 or all of them. Obviously there are more terms to the sequence so that can not be the answer. Stick with me here because this might be confusing but we already have 6 terms so there are 44 remaining, the remaining positive terms (22 of them!) will be OVER 100. For example the term after -64 is positive 128. So positive terms will no longer be under 100. The remaining negative terms (22 of them!) will obviously be under 100. So the remaining 22+ the previous 6 we counted= 28 terms under 100.</p>
<p>ohh!!
Got it!! wow, i completely forgot to include the negatives after the 128… haha wow
twinkie moment, thank you so much! (:</p>