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

User Dynde
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Answer:

see explanation

Explanation:

The n th term of an arithmetic progression is


a_(n) = 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

User Kunal Patil
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