Question

find the sum of first 24 terms of an ap it is known that 1st + 5th + 15th + 20th + 24th term is equal to 225​

Answer 1

Formula's used in calulation:

1) nth term of AP

2) Sum of n terms of AP.

Final result: Sum of first 24 terms of an AP = 900.

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Answer 2

Correct Given :-

• a₁ + a₅ + a₁₀+ a₁₅ + a₂₀ + a₂₄ = 225 .

To Find :-

• S₂₄ = ?

Formula used :-

• Tₙ = a + (n - 1)d.
• Sₙ = (n/2)[2a + (n - 1)d ]

Solution :-

→ a₁ = a

→ a₅ = a + (5 - 1)d = a + 4d

→ a₁₀ = a + (10 - 1)d = a + 9d

→ a₁₅ = a + (15 - 1)d = a + 14d

→ a₂₀ = a + (20 - 1)d = a + 19d .

→ a₂₄ = a + (24 - 1)d = a + 23d.

Adding All we get :-

→ a + a + 4d + a + 9d a + 14d + a + 19d + a + 23d = 225

→ 6a + 69d = 225

→ 3(2a + 23d) = 225

→ (2a + 23d) = 75 ---------------------- Equation ❶

____________________________

Now,

→ S₂₄ = (24/2) [ 2a + (24 - 1)d ]

→ S₂₄ = 12 [2a + 23d]

Putting value of Equation ❶ now, we get,

→ S₂₄ = 12 * 75

→ S₂₄ = 900. (Ans).

Hence, Sum of First 24 Terms of AP will be 900.