Answer:
d = 3 , a₁ = 1
Explanation:
the nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
(10)
given a₄ = 10 and a₁₂ = 34 , then
a₁ + 3d = 10 → (1)
a₁ + 11d = 34 → (2)
solve the equations simultaneously to find d and a₁
subtract (1) from (2) term by term to eliminate a₁
(a₁ - a₁) + (11d - 3d) = 34 - 10
0 + 8d = 24
8d = 24 ( divide both sides by 8 )
d = 3
(11)
substitute d = 3 into either of the 2 equations and solve for a₁
substituting into (1)
a₁ + 3(3) = 10
a₁ + 9 = 10 ( subtract 9 from both sides )
a₁ = 1