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Question
Find the missing number in the series 3, 6, 18, 72, 360, _
720
2160
1440
1860
ANSWER : 2
Descrption
<p><br> </p><p style="margin-left:0px;">The missing number in the series 3, 6, 18, 72, 360, _ is <strong>2160</strong>.</p><p style="margin-left:0px;">This is a geometric sequence with a common ratio of 3. To find the next number, we can use the following formula:</p><p>a_n = a_1 r^{n - 1} </p><p style="margin-left:0px;">where:</p><ul><li><i>an</i> is the $n$th term of the sequence</li><li><i>a</i>1 is the first term of the sequence</li><li><i>r</i> is the common ratio of the sequence</li><li><i>n</i> is the term number</li></ul><p style="margin-left:0px;">In this case, we have:</p><ul><li><i>a</i>1=3</li><li><i>r</i>=3</li><li><i>n</i>=6</li></ul><p style="margin-left:0px;">Substituting these values into the formula, we get:</p><p>a_{6} = 3 \cdot 3^{6 - 1} = 2160 </p><p style="margin-left:0px;">Therefore, the missing number in the series is <strong>2160</strong>.</p>
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