For positive integers n, the integer part of the nth term of sequence C equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, C_1 = 1.2345678…, while C_2 = 2.4681012… The sum of the first seven terms of sequence C is between: Options.
A) 28 and 29 B) 29 and 30 C) 30 and 31 D) 31 and 32 E) 32 and 33
First, construct the first seven terms, though only out to a few decimal places, following the given pattern.   C_1 = 1.23…   C_2 = 2.46…   C_3 = 3.69…   C_4 = 4.812…   C_5 = 5.10…   C_6 = 6.12…   C_7 = 7.14…   Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.   1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1= 
<gadget id="calculator">1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1</gadget>
<output>30.3</output>
30.3   Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.   The correct answer is 30 and 31.
<result>C</result>
For positive integers n, the integer part of the nth term of sequence C equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, C_1 = 1.2345678…, while C_2 = 2.4681012… The sum of the first seven terms of sequence C is between: