<p>For one of the practice tests, I got this wrong and I don’t understand their explanation. Can anyone help?</p>
<li><pre><code>In an arithmetic sequence, a5 = a10 3 and a3 = 2. Between which two consecutive terms does 0 lie?
</code></pre>
<p>(A) a4 and a5
(B) a5 and a6
(C) a6 and a7
(D) a7 and a8
(E) a9 and a10</p></li>
</ol>
<p>You left this question blank. You should have selected C.</p>
<p>Explanation</p>
<p>Because this is an arithmetic sequence, the difference between consecutive terms is constant. The first step in answering the question is finding this common difference. By knowing a5 = a10 3, set up and solve the equation an+1 an = 3/105 = 0.6. Now list the terms of the sequence, starting with a3. a3 = 2, a4 = 1.4, a5 = 0.8, a6 = 0.2, a7 = 0.4, and so on. The question is answered: 0 lies between the sixth and seventh terms of the sequence.</p>
<p>well if a5 = a10 - 3 then a5 + 3 = a10
since it’s arithmetic you also know that a5 + 5d = a10 so 5d = 3 so d = 0.6</p>
<p>so a3 = -2
a4 is going to equal a(n-1) + 0.6 = -1.4
a5 = -0.8
a6 = -0.2
a7 = 0.4</p>
<p>so between a6 and a7 you have a 0</p>
<p>Thanks! That was much easier to understand than their explanation.</p>
<p>I’ve got another question, if anyone can answer it. </p>
<ol>
<li><p>In an arithmetic sequence an, a7 = a3 + 18 = 4, which of the following equations is true?</p>
<p>(A) an = 5 + 4n
(B) an = 27.5 + 4n
(C) an = 5 + 4.5n
(D) an = 27.5 + 4.5n
(E) an = 27.5 + 6n</p></li>
</ol>
<p>The answer is D.</p>
<p>Sparknotes uses an = dn + x for their equation to find out the value of the first term in the sequence, so in this case, 7 = (4.5)(7) + x. They get -27.5 for x which is right. However, the Barron’s book uses the equation tn = t1 + (n-1)d, so that it would look like 7 = x + (6)(4.5), and x would equal -23. Which one is correct for use on the actual exam?</p>