Question

Find the sum of the first three terms of the series represented by the formula 4(- 1)(n - 1).

Answer 1

Since the question given 4( -1)(n - 1) has n to the power of 1, it means that it is a number sequence based on an Arithmetic Progression. An Arithmetic Progression is a number sequence with a constant difference.

Given that the formula is 4( -1)(n - 1),

Find the first term:

First term, n = 1

First term = 4(-1)(1 - 1)

First term = 0

Find the second term:

Second term, n = 2

Second term = 4(-1)(2 - 1)

Second term = -4

Find the third term:

Third term, n = 3

Third term = 4(-1)(3 - 1)

Third term = -8

Find the sum of these 3 terms:

Sum = 0 + (-4) + (-8)

Sum = -12

Answer: The sum of these 3 terms is -12.

Answer 2

Question

Find the sum of the first three terms of the series represented by the formula 4(- 1)(n - 1).

Solution

The sum of the first three terms is - 12

Given

The sequence is defined by the expression : 4(- 1)(n - 1)

To finD

Sum of first three terms of the sequence

Let the first,second and third terms be a,a' and A respectively

Putting n = 1,we get the first term :

a = 4( - 1)(1 - 1)

→ a = 0

Putting n = 2,

a' = 4(- 1)(2 - 1)

→ a' = 4(-1)(1)

→a' = - 4

Putting n = 3,

A = 4(-1)(3-1)

→ A =4(-1)(2)

→ A = - 8

The three terms are 0, -4 and - 8

Now,

Sum Of The Three Terms : a + a' + A

→ S = 0 - 4 - 8

→ S = - 12