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If 15 times the 15th term of an A.P. is equal to 10 times its 10th term, then find its 25th term?
Most Upvoted Answer
If 15 times the 15th term of an A.P. is equal to 10 times its 10th ter...
Explanation:
Let us assume that the first term of the A.P. is 'a' and the common difference is 'd'.
Finding the 10th term:
The 10th term of the A.P. can be represented as:
T10 = a + (10-1)d
T10 = a + 9d
Finding the 15th term:
The 15th term of the A.P. can be represented as:
T15 = a + (15-1)d
T15 = a + 14d
Using the given information:
Now, we know that 15 times the 15th term of the A.P. is equal to 10 times its 10th term.
15 * T15 = 10 * T10
15 * (a + 14d) = 10 * (a + 9d)
Simplifying this equation, we get:
5a = 5d
a = d
Finding the 25th term:
Now, we need to find the 25th term of the A.P.
The 25th term of the A.P. can be represented as:
T25 = a + (25-1)d
T25 = a + 24d
Substituting the value of 'a' as 'd', we get:
T25 = d + 24d
T25 = 25d
Therefore, the 25th term of the A.P. is 25 times the common difference 'd'.
Answer:
Hence, we can say that the 25th term of the A.P. is 25 times the common difference 'd'. To find the actual value of the 25th term, we need to know either the first term or the common difference.
Community Answer
If 15 times the 15th term of an A.P. is equal to 10 times its 10th ter...
We know that the n
th
term of the arithmetic progression is given by a+(n−1)d
Given that the 10 times the 10
th
term is equal to 15 times the 15
th
term
Therefore, 10(10
th
term)=15(15
th
term)
⟹10(a+(10−1)d)=15(a+(15−1)d)
⟹10(a+9d)=15(a+14d)
⟹10a+90d=15a+210d
⟹15a−10a=90d−210d
⟹5a=−120d
⟹a=−24d -----(1)
The 25
th
term is a+(25−1)d=a+24d=−24d+24d=0
Therefore, the 25
th
term of the A.P. is zero
th
term of the arithmetic progression is given by a+(n−1)d
Given that the 10 times the 10
th
term is equal to 15 times the 15
th
term
Therefore, 10(10
th
term)=15(15
th
term)
⟹10(a+(10−1)d)=15(a+(15−1)d)
⟹10(a+9d)=15(a+14d)
⟹10a+90d=15a+210d
⟹15a−10a=90d−210d
⟹5a=−120d
⟹a=−24d -----(1)
The 25
th
term is a+(25−1)d=a+24d=−24d+24d=0
Therefore, the 25
th
term of the A.P. is zero
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If 15 times the 15th term of an A.P. is equal to 10 times its 10th term, then find its 25th term?
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If 15 times the 15th term of an A.P. is equal to 10 times its 10th term, then find its 25th term? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 15 times the 15th term of an A.P. is equal to 10 times its 10th term, then find its 25th term? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 15 times the 15th term of an A.P. is equal to 10 times its 10th term, then find its 25th term?.
If 15 times the 15th term of an A.P. is equal to 10 times its 10th term, then find its 25th term? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 15 times the 15th term of an A.P. is equal to 10 times its 10th term, then find its 25th term? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 15 times the 15th term of an A.P. is equal to 10 times its 10th term, then find its 25th term?.
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