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If a1, a2,a3,. are in A.P, such that a1 a5 a10 a15 a20 a24=225, then a1, a2,a3,. a23 a24 is equal to A) 909 B)75 C)750 D)900 Please give answer with explanation?
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If a1, a2,a3,. are in A.P, such that a1 a5 a10 a15 a20 a24=225, then a...
Solution:

Given, a1, a2,a3,. are in A.P such that a1 a5 a10 a15 a20 a24=225.

Let, d be the common difference.

We know that,

a5 = a1 + 4d
a10 = a1 + 9d
a15 = a1 + 14d
a20 = a1 + 19d
a24 = a1 + 23d

Now,

a1 a5 a10 a15 a20 a24 = 225

a1 (a1 + 4d) (a1 + 9d) (a1 + 14d) (a1 + 19d) (a1 + 23d) = 225

On simplifying, we get

(a1 + 11d)^2 (a1 + 7d)(a1 + 17d) = 225

As the terms are in A.P, the difference between a1 and a24 is 23d.

So, a23 = a1 + 22d

Now,

a1 a2 a3 ... a23 a24 = a1 (a1 + d) (a1 + 2d) ... (a1 + 22d) (a1 + 23d)

= (a1 + 11d - 11d) (a1 + 11d - 10d) (a1 + 11d - 9d) ... (a1 + 11d + 11d) (a1 + 11d + 12d)

= (a1 + 11d)^2 (a1 - 11d)(a1 - 9d) ... (a1 + 11d)(a1 + 12d)

= (225/225) (a1 + 11d)^2 (a1 - 11d)(a1 - 9d) ... (a1 + 11d)(a1 + 12d)

= 1 x 225

= 225

Therefore, a1 a2 a3 ... a23 a24 = 225.

Hence, the answer is option B) 75.
Community Answer
If a1, a2,a3,. are in A.P, such that a1 a5 a10 a15 a20 a24=225, then a...
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If a1, a2,a3,. are in A.P, such that a1 a5 a10 a15 a20 a24=225, then a1, a2,a3,. a23 a24 is equal to A) 909 B)75 C)750 D)900 Please give answer with explanation?
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If a1, a2,a3,. are in A.P, such that a1 a5 a10 a15 a20 a24=225, then a1, a2,a3,. a23 a24 is equal to A) 909 B)75 C)750 D)900 Please give answer with explanation? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a1, a2,a3,. are in A.P, such that a1 a5 a10 a15 a20 a24=225, then a1, a2,a3,. a23 a24 is equal to A) 909 B)75 C)750 D)900 Please give answer with explanation? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a1, a2,a3,. are in A.P, such that a1 a5 a10 a15 a20 a24=225, then a1, a2,a3,. a23 a24 is equal to A) 909 B)75 C)750 D)900 Please give answer with explanation?.
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