Answer:
The first term is -49.
Solution:
aₙ = a₁ + d (n-1)
wherein
aₙ= nth term
a₁= 1st term
d= common difference
a₁₀ = a₁ + d (n-1)
19 = a₁ + d (10-1)
19 = a₁ + 9d
a₁₉ = a₁ + d (n-1)
87 = a₁ + d (19-1)
87 = a₁ + 18d
Subtract.
87 = a₁ + 18d
-19 = a₁ + 9d
68= 9d
68/9 = d
Substitute the value of d and find a₁ using any of the given terms.
a₁₀ = a₁ + d (n-1)
19 = a₁ + 68/9 (10-1)
19 = a₁ + 68/9 (9)
19 = a₁ + 68
19 - 68 = a₁
a₁ = -49
Check by finding the other given term (optional).
a₁₉ = a₁ + d (n-1)
a₁₉ = -49 + 68/9 (19-1)
a₁₉ = -49 + 68/9 (18)
a₁₉ = -49 + 136
a₁₉ = 87
