Answer:
a₁₃ = 216
Explanation:
the nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
we require to find a₁ and d before we can find a₁₃
given a₃ = 96 and a₇ = 144 , then
a₁ + 2d = 96 → (1)
a₁ + 6d = 144 → (2)
subtract (1) from (2) term by term to eliminate a₁
(a₁ - a₁) + (6d - 2d) = 144 - 96
0 + 4d = 48
4d = 48 ( divide both sides by 4 )
d = 12
substitute d = 12 into either of the 2 equations and solve for a₁
substituting into (1)
a₁ + 2(12) = 96
a₁ + 24 = 96 ( subtract 24 from both sides )
a₁ = 72
Then
a₁₃ = 72 + (12 × 12) = 72 + 144 = 216