Question

Find the sum of the first 6 terms of the series.

3-6+12-24+....

a.
–65
c.
–62
b.
–64
d.
–63


Please select the best answer from the choices provided

a) A
b) B
c) C
d) D

Answer 1

Answer: Option d. (-63) is the sum of first 6 terms

Explanation:

Given sequence is 3-6+12-24+...........

We know the formula for the sum of the sequence be

S(6) = A(1)×
`(1-r^(n) )/(1-r)`

From the given question n= 6

A(1) = 3

and common ratio r = (-6)/3 = (-2)

Now we put these values in the formula

S(6) = 3×
`(1-(-2)^(6) )/(1-(-2))`

= 3×
`((1-(-2)^(6) )/(3)`

= 3×(1-64)/3

= 3×(-63)/3

= (-63)

So the sum of six terms is (-63).

Answer 2

Option d. -63

Explanation:

a1=3

a2=-6

a3=12

a4=-24

a2/a1=(-6)/(3)→a2/a1=-2

a3/a2=(12)/(-6)→a3/a2=-2

a4/a3=(-24)/(12)→a4/a3=-2

r=a2/a1=a3/a2=a4/a3→r=-2

a5=r*a4=(-2)(-24)→a5=48

46=r*a5=(-2)(48)→a6=-96

Sum of the first 6 terms of the series: S=?

S=a1+a2+a3+a4+a5+a6

S=3-6+12-24+48-96

S=-63

Answer: Option d. -63