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3 years ago

8

I need help with the evens in that picture

1 answer:

Gelneren [198K]3 years ago

5 0

i would help you but i cannot see the image.

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The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

3 years ago

A trampoline gym charges $6 for

zhuklara [117]

Answer:

$12

Step-by-step explanation:

Assuming you meant $6 per 1/2 hour

since by multiplying 1/2 by 2 we get 1 ( our unit rate) 6*2 = 12

whole number

12

fraction

12/1

Brainliest would be appreciated if this is helpful. Let me know if you have more questions

Hope this helps!

4 0

2 years ago

Jaxon bought a book for $6 and 5 movies. He spent a total of $41. How much did each movie cost?

Vsevolod [243]

Answer: each movie costs 7$

Step-by-step explanation: 41-6=35 and you divide that by 5 which is 7

6 0

3 years ago

Read 2 more answers

Write the equation of the line that goes through (-4,13) and (8,49).

algol [13]

Answer:

y=3x +25

Step-by-step explanation:

First calculate the slope:

m = (y1 - y2)/(x1-x2)

m = (49 - 13)/(8-(-4))

m= 36/12 = 3

so we have

y = 3x + b

subtitute a point:

49=3(8) + b

b=25

the equation is y=3x +25

4 0

3 years ago

Multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial. Determine the degree and

GrogVix [38]

I think this attachment will help you

6 0

4 years ago