Answer:
[tex]\sum\limits_{i=1}^{10}(1-2i)=-100[/tex].
Step-by-step explanation:
The given expression is
[tex]\sum\limits_{i=1}^{10}(1-2i)[/tex]
We need to find first 3 terms, then we have evaluate the value.
Here,
[tex]a_i=1-2i[/tex]
For i=1,
[tex]a_1=1-2(1)=1-2=-1[/tex]
For i=2,
[tex]a_2=1-2(2)=1-4=-3[/tex]
For i=3,
[tex]a_3=1-2(3)=1-6=-5[/tex]
So first three terms are -1,-3,-5. It is an AP with first term -1 and common difference -2. So, next 7 terms are -7,-9,-11,-13,-15,-17,-19.
Now,
[tex]\sum\limits_{i=1}^{10}(1-2i)=(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)+(-15)+(-17)+(-19)[/tex]
[tex]\sum\limits_{i=1}^{10}(1-2i)=-100[/tex]
Therefore, the value of [tex]\sum\limits_{i=1}^{10}(1-2i)[/tex] is -100.
