Tag: geometric sequences

Quizzes (2) Questions (161)

Questions Related to geometric sequences

Multiple choice maths geometric sequences sum of terms of g.p sum of n terms of an gp summing geometric series

The sum of $6^{th}$ term in the geometric series $4, 12, 36...$ is

  1. $1456$
  2. $2456$
  3. $3456$
  4. $4456$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given sequence is $4,12, 36$
To find the sum of the first $S _n$ terms of a geometric sequence using the formula
Here $a = 4, r = 3, n = 6$
We know $S _n = \dfrac{a _1(1-r^n)}{1-r}$
$\Rightarrow S _6 = \dfrac{4(1-3^{6})}{1-3}$
$\Rightarrow S _6 = \dfrac{-2912}{-2}$
$\Rightarrow S _6 = 1456$

Multiple choice maths geometric sequences sum of terms of g.p sum of n terms of an gp summing geometric series

The sum of first $n$ terms of an G.P. is

  1. $S _n = \cfrac{a _1(1-r^n)}{1-r}$
  2. $S _n = \cfrac{a _1(1+r^n)}{1-r}$
  3. $S _n = \cfrac{a _1(1-r^n)}{1+r}$
  4. $S _n = \cfrac{a _1(1-r^n)}{r-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A GP can be written as:

$a,ar,ar^2, ar^3..............,ar^{n-1}$
$\text{sum} = a+ar+ar^2+ar^3+.........+ar^{n-1}$
$\text{sum} = a(r^{n-1}+r^{n-2}+r^{n-3}+r^{n-4}+...........+r+1)$
We know that:
$\dfrac{x^n -1}{x-1} = x^{n-1}+x^{n-2}+x^{n-3}+.............+x+1$
Thus $\text{sum} = a\left (\dfrac{r^n -1}{r-1}\right)$

Multiple choice maths geometric sequences sum of terms of g.p sum of n terms of an gp summing geometric series

A rubber ball is dropped from a height of $10$ meters. If the ball always rebounds $\dfrac {4}{5}$ the distance it has fallen, calculate, how far, in meters, will the ball have travelled at the moment it hits the ground for the fourth time?

  1. $4.10$
  2. $5.12$
  3. $29.52$
  4. $43.92$
  5. $49.04$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation
  • for the first time it hits the ground , it travels $10$ m
  • for the second time it hits the ground , it travels $2 \times 4/5 \times 10 = 16+10 =26$
  • for the third time it hits the ground , it travels $ 2\times 4/5 \times 4/5 \times 10 +26 =64/5+26 = 38.8$
  • for the fourth time it hits the ground , it travels $2 \times 4/5 \times 4/5 \times 4/5 \times 10 +38.8 = 256/25 + 38.8 =49.04$

Multiple choice maths geometric sequences sum of terms of g.p sum of n terms of an gp summing geometric series

Find the sum of odd integers between $1$ and $1000$ which are divisible by $3$.

  1. $83667$
  2. $54954$
  3. $99994$
  4. $79894$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Odd integers divisible by 3 are: $3,9,15,21.....999$
Let $a=3$   and   $d=6$
$\therefore T _n=999=3+(n-1)6$
$\Rightarrow n-1=\dfrac{996}{6}=166$
$\therefore n=167$
$\therefore S _n=\dfrac{167}{2}[2\times 3+(167-1)6]=83667$