Answer :
Answer:
a₁ = - 16 , a₂₁ = 24
Step-by-step explanation:
The nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₂ = - 14 , then
a₁ + d = - 14 → (1)
The sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
Given S₂₁ = 84 , then
[tex]\frac{21}{2}[/tex] [ 2a₁ + (n - 1)d ] = 84 ( multiply both sides by 2 )
21(2a₁ + 20d) = 168 ( divide both sides by 21 )
2a₁ + 20d = 8 → (2)
From (1) d = - 14 - a₁ ← substitute into (2)
2a₁ + 20(- 14 - a₁) = 8 , that is
2a₁ - 280 - 20a₁ = 8
- 18a₁ - 280 = 8 ( add 280 to both sides )
- 18a₁ = 288 ( divide both sides by -18 )
a₁ = - 16
Substitute a₁ = - 16 into (1)
- 16 + d = - 14 ( add 16 to both sides )
d = 2
Then
a₂₁ = - 16 + 20(2) = - 16 + 40 = 24