Flip Flip Flip....

$\text{Group all negative and group all positive.}$

$(-5 - 19 - 33 - 47 - … - 2007) + (12 + 26 + 40 + … + 2014)$

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$\text{Find the number of terms in the series} -5, -19, -33, … -2007.$

$\text{a}_\text{n} = \text{a}_1 + (\text{n} - 1)\text{d}$

$-2007 = -5 + (\text{n}-1)(-14)$

$\boxed{n = 144}$

$\text{Rewriting the expression, }$

$(-5 + 12) + (-19 + 26) + (-33 + 40) + … (-2007 + 2014)$

$\text{The expression simplified to }$ $(7) + (7) + (7) + … (7)$

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$\text{Counting }(-5 + 12) \text{ as the first term, that means }$

$(-2007 + 2014)\text{ is the } n^{th} \text{term (which is }\color{#0000ff}{\bf{n = 144}})$

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$\text{Therefore, there are 144 counts of 7’s. And 144 times 7 is equal to }$ $\underline{1}008.$

$\text{The first digit of the sum of the expression is 1.}$

I solved this way:

Write the sum as $S=\;(-5+12)+(-19+26)+(-33+40)+\cdots(-2007+2014)$

$S=\;7+7+\cdots$ upto $144$ times, since there are $144$ such pairs. So $S=\;7\times144=1008$ . That implies the answer is $1$ .