Question

List the first 3 terms, then evaluate

Answer 1

Answer:

$\sum\limits_{i=1}^{10}(1-2i)=-100$.

Step-by-step explanation:

The given expression is

$\sum\limits_{i=1}^{10}(1-2i)$

We need to find first 3 terms, then we have evaluate the value.

Here,  

$a_i=1-2i$

For i=1,

$a_1=1-2(1)=1-2=-1$

For i=2,

$a_2=1-2(2)=1-4=-3$

For i=3,

$a_3=1-2(3)=1-6=-5$

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,  

$\sum\limits_{i=1}^{10}(1-2i)=(-1)+(-3)+(-5)+(-7)+(-9)+(-11)+(-13)+(-15)+(-17)+(-19)$

$\sum\limits_{i=1}^{10}(1-2i)=-100$

Therefore, the value of $\sum\limits_{i=1}^{10}(1-2i)$ is -100.