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If the 10 times of the 10th term of an AP is equal to 15 times to the 15th term, then 25th term is :?
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If the 10 times of the 10th term of an AP is equal to 15 times to the ...
Given:
The 10 times of the 10th term of an arithmetic progression (AP) is equal to 15 times the 15th term.
To find:
The 25th term of the arithmetic progression.
Approach:
1. Let's assume that the first term of the AP is 'a' and the common difference is 'd'.
2. The 10th term of the AP can be represented as:
T10 = a + 9d
3. The 15th term of the AP can be represented as:
T15 = a + 14d
4. According to the given condition, 10 times T10 is equal to 15 times T15:
10(a + 9d) = 15(a + 14d)
5. Simplifying the equation, we get:
10a + 90d = 15a + 210d
5a = 120d
a = 24d
6. Now, we know that the first term 'a' is equal to 24 times the common difference 'd'.
7. The 25th term of the AP can be represented as:
T25 = a + 24d
8. Substituting the value of 'a' from step 6, we get:
T25 = 24d + 24d
T25 = 48d
Calculation:
The 25th term of the arithmetic progression is 48 times the common difference 'd'.
Conclusion:
Therefore, the 25th term of the arithmetic progression is 48d.
The 10 times of the 10th term of an arithmetic progression (AP) is equal to 15 times the 15th term.
To find:
The 25th term of the arithmetic progression.
Approach:
1. Let's assume that the first term of the AP is 'a' and the common difference is 'd'.
2. The 10th term of the AP can be represented as:
T10 = a + 9d
3. The 15th term of the AP can be represented as:
T15 = a + 14d
4. According to the given condition, 10 times T10 is equal to 15 times T15:
10(a + 9d) = 15(a + 14d)
5. Simplifying the equation, we get:
10a + 90d = 15a + 210d
5a = 120d
a = 24d
6. Now, we know that the first term 'a' is equal to 24 times the common difference 'd'.
7. The 25th term of the AP can be represented as:
T25 = a + 24d
8. Substituting the value of 'a' from step 6, we get:
T25 = 24d + 24d
T25 = 48d
Calculation:
The 25th term of the arithmetic progression is 48 times the common difference 'd'.
Conclusion:
Therefore, the 25th term of the arithmetic progression is 48d.
Community Answer
If the 10 times of the 10th term of an AP is equal to 15 times to the ...
10.t10=15.t15=>10(a+9d)=15(a+14d)==>a+24d=0=t25
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If the 10 times of the 10th term of an AP is equal to 15 times to the 15th term, then 25th term is :?
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If the 10 times of the 10th term of an AP is equal to 15 times to the 15th term, then 25th term is :? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the 10 times of the 10th term of an AP is equal to 15 times to the 15th term, then 25th term is :? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the 10 times of the 10th term of an AP is equal to 15 times to the 15th term, then 25th term is :?.
If the 10 times of the 10th term of an AP is equal to 15 times to the 15th term, then 25th term is :? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the 10 times of the 10th term of an AP is equal to 15 times to the 15th term, then 25th term is :? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the 10 times of the 10th term of an AP is equal to 15 times to the 15th term, then 25th term is :?.
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