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my bad for the lacking explanation
I'm bad with words so I'll give an example

say we have the following sequence : 
    𝑎𝑛=1+(𝑛−1)*2
    thus 𝑎𝑛=2*𝑛-1

and the following function : 
    X𝑛 = 𝑎𝑛^2 + 12 * 𝑎𝑛 + 7
    thus X𝑛 = 4*𝑛^2 + 20*𝑛 - 4

how do I get the sum of say the first 10 terms :
    sum Xn from n = 1 to n = 10

Thank You

DOG can only occupy one position in the leter group as there are only three letters allowed

    4 numbers would be   10 000 possibilities     (0000 - 9999)

soooo     26 x 26 x 26  x 10 000   -   10000

top triangle    1/2 b * h =     1/2 7 * 2

rectangle below        2 x 7

bottom rectangle   3 x 2

 small square on L   1x1       add 'em all together

There are 3! ways to chose the first row

For each of those there is 2 ways to chose the second row.

Then the last row is fixed.

So how many is that ?

\(\frac{4645*598}{58598}-565+265\approx-252.6\)

Assuming that this is a 20-21-29 triangle, of which we have side lengths 80, 4*21, and 116, we have 80+84+116=280

-7400845/29299

36 possible rolls

ways to roll a sum of 10

64

46

55

   three ways   out of 36    3/36 =   1/12

log(b/a) = log(b) - log(a)

so

log₂(2/1) = log₂(2) - log₂(1)

log₂(3/2)=log₂(3) - log₂(2)

...

log₂(2010/2009) = log₂(2010) - log₂(2009)

Adding up all these, resuts in most of them cancelling out, and we are left with

log₂(2010) - log₂(1)  

Now 2¹⁰ = 1024 and 2¹¹ = 2048, so I'll leave you to decide the final steps.

It must read Ax + Bx = -1

Deleted. Misinterpreted the question!

In base 10 we use the digits   0,1,2,3,4,5,6,7,8,9     there are 10 of them

In base 14 we need 14 digits.   Thez can be 0,1,2,3,4,5,6,7,8,9,A;B;C;D

The biggest 3 digit one is     DDD (base14)

the biggest one in base 10 would be 999 .

Ths is    \(9*10^2+9*10+9\)

the biggest one base 14 would be DDD

Converting this to base 10 gives     \(13*14^2+ 13*14+13\)

--------------------------------------

Sorry I have given you the biggest 3 digit base 14 number, converted to base 10

The smalles one would be   100 (base 14)

where  the place value of the 1 is  14^2    (That is in base 10)

If I have just confused you let me know and I will explain it better.  Think about it first though.

180°-115° = 65°

z = 180° - 56° - 65°

z = 59°

BC = m;op[=679=\]u5zcb520

3x - 22 = 80 + x

2x = 102

x = 51

By  Angle sum property of triangles,

4x - 22 + 10x - 4 + x +11 = 180

⇒15x - 15                         = 180

⇒15x                                = 165

       x                                = 11

This is a question almost everybody goes through, extremely simple inequalities, but not a website everyone finds out early or late. DONT MAKE FUN OF SOMEONE'S INTELLECTUAL ABILITY

$2x-3y=9, -5x-3y=30$

$(2x-3y)-(-5x-3y)=-21,$

$7x=-21$

$\boxed{x=-3,y=-5}$

2x - 3y = 9                 ...(1)

-5x - 3y = 30              ...(2)

Subtracting (1) from (2)

     -5x - 3y = 30

-     2x - 3y = 9

       -7x       = 21

          x      = -3

By Linear pair property, 

angle adjacent to (3x-22) = 180 - 3x + 22

                                         = 202 - 3x

By Angle sum property of triangles,

202 - 3x + x + 80 = 180

⇒282 -2x = 180

⇒2x         = 282 - 180

⇒ 2x         = 102

      x         = 51º

$62=3y+2$
$62-2=3y+2-2$

$60=3y$

$60/3=3y/3$
$\boxed{20=y | y=20}$
 

We can see 180-(3x-22) is the angle in the triangle, this results in 180+22-3x= 202-3x, we add the three angles giving 202-3x+x+80=180,

282-2x=180

-2x=-102

x=61

[UVRW] = 1/2