<h3>Original Equation:</h3>
<h3>Steps:</h3>
<em>*To solve for a variable, isolate the desired variable onto one side.</em>
Firstly, we want to add 1/3 to each side however -5/6 and 1/3 do not share the same denominator, and we want them to have that and we can do that by finding the LCD, or lowest common denominator. To find the LCD, list the multiples of 6 and 3 and the lowest multiple that they share is their LCD. In this case, their LCD is 6. Multiply -1/3 by 2/2:
Now that we have common denominators, add both sides by 2/6:
Next, you want to cancel out 2 to isolate z. Usually, one would divide both sides by 2, however remember that <u>dividing by a number is the same as multiplying by it's reciprocal.</u> To find a number's reciprocal, flip the numerator and denominator around. In this case, since 2 is a <em>whole number</em> this means that the denominator is 1. In this case: 2/1 would become 1/2. Multiply both sides by 1/2:
<h3>Final Answer:</h3>
<u>Your final answer is z = -1/4.</u>
Q1)
the sequence should start with 10, after that each term is calculated by subtracting 3 from the previous term.
1st term - 10
2nd term - 10 - 3 = 7
3rd term - 7 - 3 = 4
4th term - 4 - 3 = 1
5th term - 1 - 3 = -2
6th term - -2 - 3 = -5
7th term - -5 - 3 = -8
8th - -8 - 3 = -11
9th - -11 - 3 = -14
10th -14 - 3 = -17
the sequence is - 10,7,4,1,-2,-5,-8,-11,-14,-17
Q2)
<span>the sequence whose nth term is the sum of the first n positive integers
In this we get the term by adding all the integers of the terms before that term
1st term - n = 1 no terms before this , therefore 0 + n(1) = 1
2nd term -n =2 sum of integers before - 1 + n( 2) = 3
3rd - 3+3 = 6
4th - 6+4 = 10
5th - 10 + 5 = 15
6th - 15 + 6 = 21
7th - 21 + 7 = 28
8th - 28 + 8 = 36
9th - 36 + 9 = 45
10th - 45 + 10 = 55
this is a triangular number pattern
this number pattern can be found out using ; n = (n x (n+1))/2
sequence is - 1,3,6,10,15,21,28,36,45,55
Q3)
</span>the sequence whose nth term is 3n − 2n
general term for this sequence is 3n − 2n
to find 1st term , n = 1
substituting n = 1 in the general term
1st term - 3x1 - 2x1 = 3-2 = 1
2nd - 3x2- 2x2 = 6 - 4 = 2
3rd - 3x3 - 2x3 = 9-6 = 3
4th - 3x4 - 2x4 = 12 - 8 = 4
5th - 3x5 - 2x5 = 15 - 10 = 5
6th - 3x6 - 2x6 = 18 - 12 = 6
7th - 3x7 - 2x7 = 21 - 14 = 7
8th - 3 x8 - 2x8 = 24 - 16 = 8
9th - 3x9 - 2x9 = 27 - 18 = 9
10th - 3x10 - 2x10 = 30-20 = 10
sequence is 1,2,3,4,5,6,7,8,9,10
Q4)
<span>the sequence whose nth term is √ n
when n=1 1st term is </span>√1 = 1
1st term - √1 = 1
2nd term - √2 = 1.41
3rd - √3 = 1.73
4th - √4 = 2
5th - √5 = 2.23
6th- √6 = 2.44
7th - √7 = 2.65
8th- √8 = 2.82
9th - √9 = 3
10th - √10 = 3.16
The sequence is 1, 1.41, 1.73, 2, 2.23, 2.44, 2.65, 2.82, 3, 3.16
Q5)T<span>he sequence whose first two terms are 1 and 5 and each succeeding term is the sum of the two previous terms
</span>1st term - 1
2nd term - 5
3rd term - add 1st and 2nd term (1+5) = 6
4th term - add 2nd and 3rd terms (5+6) = 11
5th - add 3rd and 4th (6+11) = 17
6th - (11+17) = 28
7th - (17 + 28) = 45
8th - 45 + 28 = 73
9th - 73 + 45 = 118
10th - 73+ 118 = 191
sequence is - 1,5,6,11,17,28,45,73,118,191
