5n + (-6) = -2
add 6 to -2
5n = -2 + 6
5n = 4
divide both sides by 5
n = 4/5
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
The amount invested in the account that yields 7% interest is $4000.
The amount invested in the account that yields 12% interest is $1000.
<h3>What are the linear equations that represent the question?</h3>
a + b = 5000 equation 1
0.07a + 0.12b = 400 equation 2
Where:
a = amount invested in the account that yields 7% interest.
b = amount invested in the account that yields 12% interest.
<h3>How much is invested at each rate?</h3>
Multiply equation 1 by 0.07
0.07a + 0.07b = 350 equation 3
Subtract equation 3 from equation 2
0.05b = 50
b = 50 / 0.05
b = 1000
Subtract 1000 from 5000: 5000 - 1000 = 4000
To learn more about linear functions, please check: brainly.com/question/26434260
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3.5 cookies
Friend one: 3 Friend two: 3
One leftover cookie
Split in half give one to each and that makes 3.5
Answer:
Her account balance after 5 years is $8702.87
Step-by-step explanation:
1500 (1.05) = 1575 --> after one year
1575 + 1500 = 3075
3075 (1.05) = 3228.75 --> after two years
3228.75 + 1500 = 4728.75
4728.75 (1.05) = 4965.1875 --> after three years
4965.1875 + 1500 = 6465.1875
6465.1875 (1.05) = 6788.44688 --> after four years
6788.44688 + 1500 = 8288.44688
8288.44688 (1.05) = 8702.86922 --> after five years = $8702.87
