Answer:
a₁ = 15
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
given S₁₄ = - 63 , then
[tex]\frac{14}{2}[/tex] [ 2a₁ + 13d ] = - 63
7(2a₁ + 13d) = - 63 ( divide both sides by 7 )
2a₁ + 13d = - 9 → (1)
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
given a₁₄ = - 24 , then
a₁ + 13d = - 24 → (2)
subtract (2) from (1) term by term to eliminate d
a₁ + 0 = - 9 - (- 24)
a₁ = - 9 + 24 = 15
