Answer:
see explanation
Step-by-step explanation:
The n th term of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₂₄ = 2a₁₀ , then
a₁ + 23d = 2(a₁ + 9d) = 2a₁ + 18d ( subtract a₁ from both sides )
23d = a₁ + 18d ( subtract 18d from both sides )
5d = a₁
Then
a₇₂ = a₁ + 71d ← substitute a₁ = 5d
= 5d + 71d
= 76d
and
a₁₅ = a₁ + 14d = 5d + 14d = 19d
Now 76d = 4 × 19d
Thus
a₇₂ = 4a₁₅
