13. If 6 times the 6th term of an A.P. is equal to

Mathematics

1 answer:

romanna [79]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

The n th term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

6(a₁ + 5d) = 13(a₁ + 12d) ← distribute parenthesis on both sides

6a₁ + 30d = 13a₁ + 156d ( subtract 13a₁ from both sides )

- 7a₁ + 30d = 156d ( subtract 30d from both sides )

- 7a₁ = 126d ( divide both sides by - 7 )

a₁ = - 18d

Now

a₁₉ = a₁ + 18d = - 18d + 18d = 0 ← as required

You might be interested in

PLEASE HELP

Readme [11.4K]

Answer:

x=5

Step-by-step explanation:

5 0

3 years ago

A small dealership leased 21 Suburu Outbacks on 2-year leases. When the cars were returned at the end of the lease, the mileage

Liula [17]

Answer:

yes 30 is the answer

Step-by-step explanation:

4 0

3 years ago

In a bag there are 10p coins, 20p coins and 50p coins

Scrat [10]

Answer:

Approximately 25p (please change to pounds by yourself I'm not European, sorry).

Ok so according to my research its 100 pence to one pound. Which will mean that 25p in pounds is £ 00.25

Step-by-step explanation:

<h3>let's say:</h3><h3>10p= <em>x</em></h3><h3>20p=<em> </em><em>y</em><em> </em></h3><h3>50p= <em>z</em><em> </em></h3><h3>'3 fewer 20p (<em>y</em><em>)</em><em> </em>coins than 10p (<em>x</em>) coins'</h3><h3>Therefore:</h3><h3>y-3=<em>x</em><em> </em></h3><h3>and <em>y</em>= <em>x</em>+3</h3><h3>'7 more 50p coins (<em>z</em>) than 10p coins (<em>x</em>)'</h3><h3>That is:</h3><h3><em>z</em>+7= <em>x</em></h3><h3><em>z</em><em>=</em><em> </em><em>x-7</em></h3><h3>'altogether are 61 coins'</h3><h3><em>x</em><em>+</em><em>y</em><em>+</em><em>z</em><em> </em><em>=</em><em> </em>61 </h3><h3>(substitute for y and z)</h3><h3><em>x</em><em> </em>+ <em>x</em><em> </em>+ 3 + <em>x</em><em> </em>- 7 = 61</h3><h3><em>x</em><em>+</em><em>x</em><em>+</em><em>x</em><em>+</em><em>3</em><em>-7</em><em> </em><em>=</em><em> </em>61</h3><h3>3<em>x</em><em> </em>- 4= 61</h3><h3>3<em>x</em>= 61 + 4</h3><h3>3<em>x</em>=65</h3><h3><em>x</em>= 65÷3</h3><h3><em>x</em>= (approximately) 21.6 </h3><h3>(Substitute <em>x</em><em> </em>in <em>y</em><em> </em>and <em>z</em>)</h3><h3><em>y</em><em> </em><em>=</em><em> </em><em>x</em><em>+</em>3</h3><h3><em>y</em><em> </em>= 21.6 + 3 = 24.6 (approximately 25)</h3><h3><em>z</em><em> </em><em>=</em><em> </em><em>x</em><em> </em>-7</h3><h3><em>z</em><em>=</em><em> </em>21.6-7= 14.6 (approximately 15)</h3><h3>y= 20p </h3><h3>y= 25p (approximately)</h3><h3 /><h3><u>Check</u><u> </u></h3><h3>x+y+z= ?</h3><h3>21.6 + 24.6 + 14.6= 60.8 (approximately 61)</h3>

(Sorry I couldn't change to pounds)

And I tried to explain as much as possible, you can ask if you're confused.

5 0

3 years ago

What is the relationship between these ratios 5/8 and 8/10 proportional or non proportional

Arlecino [84]

Non proportional. It is Non Proportinal.

6 0

3 years ago

Solve the equation.

elena55 [62]

Answer: