Question

Find the missing terms in each geometric sequence.

Answer 1

Answer:

1) 256, -128, 64, -32

2) 27, 9, 3, 1, 1/3

3) 5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰,

Step-by-step explanation:

1. In this geometric series each term is obtained by multiplying the previous term by (-1/2) or dividing by (-2).

256 ÷ (-2) = - 128

-128 ÷ (-2) = 64

64 ÷ (-2) = (-32)

The geometric series is:

     256, -128, 64, -32...

We can find the common ratio by dividing the second term by first term.

2) 27, 9, ___, _________, 1/3

       $\sf \boxed{\bf common \ ratio= \dfrac{second \ term}{first \ term}}$

                                 $\sf = \dfrac{9}{27}\\\\ = \dfrac{1}{3}$

  $\sf 9*\dfrac{1}{3}=3\\\\3*\dfrac{1}{3}=1$

The geometric series is:

  27, 9, 3, 1, 1/3....

3) 5x², _____, 5x⁶, 5x⁸, _____, ....

Here, we can take 3rd term and 4th term to find the common ratio.

  $\sf common \ ratio = \dfrac{5x^8}{5x^6}$

                       $\s = x^{8-6}\\\\=x^2$

5x² * x² = 5x⁴

8x⁸ * x² = 8x¹⁰

The geometric serious is:

5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰, ...

Answer 2

Answer's:

$\sf 1.) \ 256, -128, 64, -32,..\\ \\ 2.) \ 27, 9, 3, 1, 1/3,... \\ \\3.) \ 5x^2, 5x^4, 5x^6, 5x^8,5x^{10} , ...$

$\sf Geometric \ formula: ar^{n-1}$

• where 'a' is first term, 'r' is common ratio.

1)

Find the common ratio:

• next term ÷ previous term

• 32 ÷ -64 = -1/2

Equation: $256(-\frac{1}{2} )^{n-1}$

2nd term: $256(-\frac{1}{2} )^{2-1}=-128$

3rd term: $256(-\frac{1}{2} )^{3-1}=64$

2)

Find common ratio:

• next term ÷ previous term

• 9 ÷ 27 = 1/3

Equation: $27(\frac{1}{3} )^{n-1}$

3rd term: $27(\frac{1}{3} )^{3-1}=3$

4th term: $27(\frac{1}{3} )^{4-1}=1$

3)

Find the common ratio:

• next term ÷ previous term

• 5x^8 ÷ 5x^6 = x^2

Equation: $5x^2 (x^2)^{n-1}$

2nd term: $5x^2 (x^2)^{2-1} = 5x^2 (x^2) = 5x^{4}$

5ht term: $5x^2 (x^2)^{5-1} = 5x^2 (x^8) = 5x^{10}$