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
Answer:
20 square feet
Step-by-step explanation:
The length of a rectangular deck is five times it's width if the decks perimeter is 24 feet what is the decks area
Step 1
We find the Length and Width of the deck
Perimeter of a rectangle = 2L + 2W
The length of a rectangular deck is five times it's width
W = Width
L = Length = 5W
P = 24 feet
Perimeter = 2(5W) + 2W
24 = 10W + 2W
24 = 12 W
W = 24/12
W = 2 feet
Solving for L
L = 5W
L = 5 × 2 feet
L = 10 feet
Step 2
We find the area of the deck
Area of the deck(Rectangle) = Length × Width
= 10 feet × 2 feet
= 20 square feet