Answer:
A: an = 6n - 9
Step-by-step explanation:
third term in an arithmetic sequence is 9
a3 = a + 2d
a + 2d = 9
the fifth term is 21
a5 = a + 4d
a + 4d = 21
a + 2d = 9 (1)
a + 4d = 21 (2)
Subtract (1) from (2) to eliminate a
4d - 2d = 21 - 9
2d = 12
d = 12/2
d = 6
Substitute d = 6 into (1)
a + 2d = 9 (1)
a + 2(6) = 9
a + 12 = 9
a = 9 - 12
a = -3
nth term of this sequence = a + (n - 1)d
= -3 + (n - 1)6
= -3 + 6n - 6
= 6n - 9
an = 6n - 9
Answer:
a b c e
Step-by-step explanation:
1000 this is because it is the right one
Answer: the cost of each pencil is $0.5
the cost of each eraser is $0.15
Step-by-step explanation:
Let x represent the cost of one pencil.
Let y represent the cost of one eraser.
Becky spent $1.45 for 2 pencils and 3 erasers. This means that
2x + 3y = 1.45- - - - - - - - - -1
Luke spent $2.65 for 5 pencils and 1 eraser. This means that
5x + y = 2.65- - - - - - - - - -2
Multiplying equation 1 by 1 and equation 2 by 3, it becomes
2x + 3y = 1.45
15x + 3y = 7.95
Subtracting, it becomes
- 13x = - 6.5
x = - 6.5/- 13
x = 0.5
Substituting x = 0.5 into equation 2, it becomes
5 × 0.5 + y = 2.65
2.5 + y = 2.65
y = 2.65 - 2.5
y = 0.15
