Answer:
a₁ = - 24
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₇ = 2a₅ , then
a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )
- a₁ - 2d = 0 → (1)
The sum to n terms of an AP is
= 
[ 2a₁ + (n - 1)d ]
Given 
= 84 , then
(2a₁ + 6d) = 84
3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )
2a₁ + 6d = 24 → (2)
Thus we have 2 equations
- a₁ - 2d = 0 → (1)
2a₁ + 6d = 24 → (2)
Multiplying (1) by 3 and adding to (2) will eliminate d
- 3a₁ - 6d = 0 → (3)
Add (2) and (3) term by term to eliminate d
- a₁ = 24 ( multiply both sides by - 1 )
a₁ = - 24
Since we have the 2.1 next to the parenthesis, we need to first distribute.
2.1 * x & 2.1 * 5
2.1x + 10.5
Then we take that and add the equals seven to the problem to move onto the next step.
2.1x + 10.5 = 7
We must get the 2.1x alone, therefore subtracting the 10.5 as it will also be subtracted on the other side as well.
2.1x + 10.5 = 7
- 10.5 -10.5
2.1x = -3.5
To get the x alone, we must divide both sides by 2.1, therefore removing the 2.1 from the x.
2.1x = -3.5
/2.1 /2.1
x = 1.66666666667
Hope this helped!
- Kat
Answer:
In the picture
Step-by-step explanation:
Salary = 40hrs x 52wks x $25.21
= $<span>52,436.80 per year</span>
