the 24 term of an arithmetic progression is twice its 10th term show that its 72 term is 4 times the 15th term

see explanation

Step-by-step explanation:

The n th term of an arithmetic progression is

= 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