Simplify the following<br> (-3a^2b^6)^2

The 10th, 4th and 1st term of an A.P are three consecutive find the common ratio of the G.P and the sum of the 6th term, taking

valina [46]

Answer:

S_6 = 252

Step-by-step explanation:

We are told that the 10th, 4th and 1st term of an A.P are three consecutive terms of a G.P.

Now,formula for nth term of an AP is;

a_n = a + (n - 1)d

Thus;

a_10 = a + (10 - 1)d

a_10 = a + 9d

Also;

a_4 = a + (4 - 1)d

a_4 = a + 3d

First term is a.

Thus, since they are consecutive terms of a G.P, it means that;

(a + 9d)/(a + 3d) = (a + 3d)/a

Cross multiply to get;

a(a + 9d) = (a + 3d)(a + 3d)

a² + 9ad = a² + 6ad + 9d²

a² will cancel out to give;

9ad - 6ad = 9d²

3ad = 9d²

Divide both sides by 3d to get;

a = 3d

We are told that the first term is 4.

Thus, 4 = 3d

d = 4/3

We saw earlier that ratio of the GP is (a + 3d)/a

Thus; r = (4 + 3(4/3))/4 = 8/4 = 2

Sum of n terms of a G.P is given by;

S_n = a(rⁿ - 1)/(r - 1)

S_6 = 4(2^(6) - 1)/(2 - 1)

S_6 = 252

8 0

3 years ago

Easy:

Ugo [173]

Answer:

l x w do the the math

Step-by-step explanation:

there

4 0

3 years ago

Read 2 more answers

"Find the surface area of the following shapes. Round to the nearest tenth if necessary." Is this correct? (Bold Mikado is my wo

Ede4ka [16]

Answer:

360 cm^2

Step-by-step explanation:

First find the area of the bottom

10*10 = 100

The find the area of one of the triangular shapes

A = 1/2 bh since it is a triangle

A = 1/2 ( 10)*13 = 65

Since there are 4 triangles ( 1 for each side), multiply by 4

4*65 = 260

Add the areas together

260+100 = 360

8 0

4 years ago

1. Explain the Law of Cosines by ∆ ABC

seropon [69]

<h3>TRIGONOMETRY</h3>

===================================

1.) Explain the Law of Cosines by ∆ ABC

$\begin{gathered}\sf{{a ^ 2 = b ^ 2 + c ^ 2 - 2bc(cos A)}}\\ \sf{{b ^ 2 = a ^ 2 + c ^ 2 - 2ac(cos B)}} \\ \sf{{c ^ 2 = a ^ 2 + b ^ 2 - 2ab(cos C)}}\end{gathered}$

2.) Explain Law of Sines by ∆ ABC

$\sf{{\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}}}$

3.) Explain The SSA ( There is no SSA postulate so you may have just typed the question incorrectly or you may be asking about SSA Possibilities.)

» SSA ( Side-Side-Angle) · the two triangles are equal if two sides and an angle not included between them are equal.

<h3>The SSA Possibilities:</h3>

If ∠A is an acute angle and a≥b, then there is exactly one solution.

If ∠A is an obtuse or a right angle and a≤b, then there is exactly no solution.

If ∠A is an acute angle, a<b, and a=b sin A then there is exactly one solution.

If ∠A is an obtuse or a right angle and a>b, then there is exactly one solution.

===================================

#LetEarthBreathe

7 0

2 years ago

Read 2 more answers

15m+22=-7m+18 solve for m

Ivanshal [37]

I hope this answer your question.

6 0

3 years ago

Simplify the following (-3a^2b^6)^2