# Find the value of 1 -2 -3 + 2 -3 -4 up to 100 terms

Welcome to my article Find the value of 1 -2 -3 + 2 -3 -4 up to 100 terms. This question is taken from the simplification lesson.
The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions.
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## Find the value of 1 -2 -3 + 2 -3 -4 up to 100 terms

First write this question as follows and then solve,

\displaystyle \Rightarrow \left( {1-2-3} \right)+\left( {2-3-4} \right)+\left( {3-4-5} \right)+\left( {4-5-6} \right)+\left( {5-6-7} \right)+\left( {6-7-8} \right)+\left( {7-8-9} \right)+\left( {8-9-10} \right)+\left( {9-10-11} \right)+\left( {10-11-12} \right)+\left( {11-12-13} \right)+\left( {12-13-14} \right)+\left( {13-14-15} \right)+\left( {14-15-16} \right)+\left( {15-16-17} \right)+\left( {16-17-18} \right)+\left( {17-18-19} \right)+\left( {18-19-20} \right)+\left( {19-20-21} \right)+\left( {20-21-22} \right)+\left( {21-22-23} \right)+\left( {22-23-24} \right)+\left( {23-24-25} \right)+\left( {24-25-26} \right)+\left( {25-26-27} \right)+\left( {26-27-28} \right)+\left( {27-28-29} \right)+\left( {28-29-30} \right)+\left( {29-30-31} \right)+\left( {30-31-32} \right)+\left( {31-32-33} \right)+\left( {32-33-34} \right)+\left( {33-34-35} \right)+34

\displaystyle \Rightarrow \left( {1-2-3} \right)+\left( {2-3-4} \right)+\left( {3-4-5} \right)+…………..+\left( {33-34-35} \right)+34

here,

a = -4

d = -1

n = 33

Formula

sum = \displaystyle \frac{n}{2}\left[ {2a+\left( {n-1} \right)d} \right]

putting of value a ,d ,n in this formula,

sum \displaystyle \Rightarrow \frac{{33}}{2}\left[ {2(-4)+\left( {33-1} \right)(-1)} \right]

\displaystyle \Rightarrow \frac{{33}}{2}\left[ {-8+32(-1)} \right]

\displaystyle \Rightarrow \frac{{33}}{2}\left[ {-8-32} \right]

\displaystyle \Rightarrow \frac{{33}}{2}\left[ {-40} \right]

\displaystyle \Rightarrow \frac{{33\times -40}}{2}

\displaystyle \Rightarrow \frac{{33\times -20\times 2}}{2}

\displaystyle \Rightarrow 33\times -20

\displaystyle \Rightarrow -660

We have already added up to the 33rd series term
So

Total sum = sum up to 33rd row term + 34

= -660 + 34

= – 626 [Answer]

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