Question

List the first 3 terms, then evaluate

Answer 1

`\sum\limits_(i=1)^(10)(1-2i)=-100`.

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.