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MathNumerator is always 1 while the denominator is a square number, thus we can write the sequence as follows `1/1^2,1/2^2,1/3^2,1/4^2,1/5^2,...` From this we see that the `n`th terms is `a_n=1/n^2`

Math`a_n=4n7` `a_1=4*17=3` `a_2=4*27=87=1` `a_3=4*37=127=5` `a_4=4*47=167=9` `a_5=4*57=207=13` So, the first five terms of the sequence are `3,1,5,9,13`

Math`3^n` is 3, 9, 27, 81 and 243. Therefore the first five terms are 21/3 = 1 and 2/3, 21/9 = 1 and 8/9, 21/27 = 1 and 26/27, 21/81 = 1 and 80/81, 21/243 = 1 and 242/243.

Math`a_n=(2)^n` `a_1=(2)^1=2` `a_2=(2)^2=2*2=4` `a_3=(2)^3=2*2*2=8` `a_4=(2)^4=2*2*2*2=16` `a_5=(2)^5=2*2*2*2*2=32` So, the first five terms of the sequence are `2,4,8,16,32`

Math`a_n=(1/2)^n` `a_1=(1/2)^1=1/2` `a_2=(1/2)^2=1/4` `a_3=(1/2)^3=1/8` `a_4=(1/2)^4=1/16` `a_5=(1/2)^5=1/32` So, the first five terms of the sequence are `1/2,1/4,1/8,1/16,1/32`

Math`a_n=n/(n+2)` `a_1=1/(1+2)=1/3` `a_2=2/(2+2)=2/4=1/2` `a_3=3/(3+2)=3/5` `a_4=4/(4+2)=4/6=2/3` `a_5=5/(5+2)=5/7` So, the first five terms of the sequence are `1/3,1/2,3/5,2/3,5/7`

MathThese terms are fractions, their numerators and denominators are easy to compute. The first five terms are 3, 12/11, 9/13, 24/47 and 15/37.

Math`(1)^n` is 1 for even n and 1 for odd n. So `1+(1)^n` is 2 or 0, respectively. So the first five terms are 0, 1, 0, 1/2 and 0.

MathThe first five terms are 1, 1/4, 1/9, 1/16 and 1/25.

Math`2x+6y=16` `2x3y=7` Write the system of equations as an augmented matrix. `[[2,616],[2,37]]` Multiply the second line by 1. `[[2,616],[2,37]]` Eliminate the first column....

MathrsWe began by stating our equations as follows: 3x  2y = 27 x + 3y = 13 (NB: Note that I wrote the values of the x variable below each other, values with the y variable below each other and the...

Math`x+y=4` `2x4y=34` Write the system of equations as an augmented matrix. `[[1,14],[2,434]]` Multiply the first line by a 2. `[[2,28],[2,434]] ` Eliminate the first column....

Math`x+2y3z=28` `4y+2z=0` `x+yz=5` The equations in the matrix form can be written as, `[[1,2,3,28],[0,4,2,0],[1,1,1,5]]` Add Row 1 and Row 3 `[[1,2,3,28],[0,4,2,0],[0,3,4,33]]` Multiply...

Math`3x2y+z=15` `x+y+2z=10` `xy4z=14` `A=[[3,2,1],[1,1,2],[1,1,4]]` `b=[[15],[10],[14]]` `[Ab]=[[3,2,1,15],[1,1,2,10],[1,1,4,14]]` Multiply 2nd Row by 3 and add Row 1...

MathThe augmented matrix is `[[1,1,22],[3,4,4],[4,8,32]]` On applying `R_1 gt R_1 ` and `R_3 gt (R_3)/4` we get (means inverse the sign of first row and divide the third row by 4)...

MathThe augmented matrix `[[1,2,0],[1,1,6],[3,2,8]]` On applying `R_2 gt R_1  R_2 ` we get `[[1,2,0],[0,1,6],[3,2,8]]` On applying `R_3 gt 3R_1  R_3 ` we get `[[1,2,0],[0,1,6],[0,8,8]]` On...

MathGiven , 2x + 6y = 22, x + 2y = 9 so A = 2 6 1 2 and B = 22 9 so the augmented matrix is A^~=[A B]= 2 6 22 1 2 9 step 1....

MathGiven system of equations are 5x  5y = 5, 2x  3y = 7 so ,we get the matrices as A= 5 5 2 3 and B= 5 7 the augmented matrix [AB] = 5 5 5...

MathGiven system of equations are 8x  4y = 7, 5x + 2y = 1 so the matrix A ,B are given as foll A = 8 4 5 2 B= 7 1 so the augmented matrix is [AB] = 8 4 7...

MathGiven system of equations are , x  3y = 5, 2x + 6y = 10 so the matrix A,B are as follows, A = 1 3 2 6 and B = 5 10 so the augmented matrix is [AB] = 1 3 5...

MathThe augmented matrix is `[[1,2,1,8],[3,7,6,26]]` On applying `R_2 gt R_2  3R_1` we get `[[1,2,1,8],[0,1,3,2]]` On applying `R_1 gt R_1  2R_2 ` we get `[[1,0,5,4],[0,1,3,2]]` The corresponding...

Math`x3z=2` `3x+y2z=5` `2x+2y+z=4` The equations can be written as `[[1,0,3,2],[3,1,2,5],[2,2,1,4]]` R2 `>` (R1+R3)R2 `[[1,0,3,2],[0,1,0,3],[2,2,1,4]]` R3 `>` (R32R2)...

Math`2xy+3z=24` `2yz=14` `7x5y=6` Write the equations as, `[[2,1,3,24],[0,2,1,14],[7,5,0,6]]` Make the pivot in the first column by dividing the First row by 2,...

MathThe augmented matrix is `[[1,1,1,14], [2,1,1,21],[3,2,1,19]] ` On applying `R_1 gt R_1 +R_2` we get (means changing 1st row as the sum of of first and second row)...

Math`2x+2yz=2` `x3y+z=28` `x+y=14` The equations can be written as, `[[2,2,1,2],[1,3,1, 28],[1,1,0,14]]` R2`>` R1+R2+R3 `[[2,2,1,2],[2,0,0,12],[1,1,0,14]]` R1 `>` R1R2...

MathThe order of a matrix is determined by the number of rows and the number of columns. This matrix has 2 rows and 2 columns. Therefore the order of the matrix is 2 X 2.

MathThe order of a matrix is determined by the number of rows and the number of columns. This matrix has 2 rows and 3 columns. Therefore the order of the matrix is 2 X 3.

MathThe order of a matrix is determined by the number of rows and the number of columns. This matrix has 3 rows and 3 columns. Therefore the order of the matrix is 3 X 3.

MathThe order of a matrix is determined by the number of rows and the number of columns. This matrix has 3 rows and 2 columns. Therefore the order of the matrix is 3 X 2.

Math`[[4,3,,5],[1,3,,12]]`

Math`[[7,422],[5,95]]`

Math`[[1,10,2,,2],[5,3,4,,0],[2,1,0,,6]]`

Math`[[1,8,5,,8],[7,0,15,,38],[3,1,8,,20]]`

Math`[[7,5,1,,13],[19,0,8,,10]]`

Math`[[3,2,3,,20],[0,25,11,,5]]`

MathThe system of linear equations represented by the augmented matrix is 1x+2y=7 2x3y=4

MathThe system of equations represented by the augment matrix is 7x5y=0 8x+3y=2

MathThe system of equations repressed by the augmented matrix is 2x+5z=12 1y2z=7 6x+3y=2

MathThe system of equations represented by the augmented matrix is 4x5y1z=12 11x+6z=25 3x+8y=29

Math`x+2y=7` `2x+y=8` `[[1,27],[2,18]]` Multiply the first line by 2. `[[2,414],[2,18]]` Eliminate the first column. `[[2,414],[0,36]]` `3y=6` `y=2` `2x4y=14` `2x4(2)=14`...

MathGiven the matrix [7, 0] The order of the matrix is determined by the number of rows and the number of columns. This matrix has 1 row and 2 columns. Therefore the order is 1 X 2.

MathThe order of a matrix is determined by the number of rows and the number of columns. This matrix has 1 rows and 4 columns. Therefore the order of the matrix is 1 X 4.

MathThe order of a matrix is determined by the number of rows and the number of columns. This matrix has 3 rows and 1 columns. Therefore the order of the matrix is 3 X 1.

MathThe order of a matrix is determined by the number of rows and the number of columns. This matrix has 3 rows and 4 columns. Therefore the order of the matrix is 3 X 4.

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