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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 the 25th term is:
- a)25 times of 25th term
- b)zero
- c)1
- d)2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the 10 times of the 10thterm of an AP is equal to 15 times to the 1...
According to question ,
10 x 10th term =15 x 15th term
let a is the first term and d is the common difference .
10 (a+9d)=15 (a+14d)
5a+120d=0
a +24d=0
now ,
25th term =a+(25-1) d=a+24d=0
hence 25th term=0
Most Upvoted Answer
If the 10 times of the 10thterm of an AP is equal to 15 times to the 1...
Problem:
If the 10 times of the 10th term of an AP is equal to 15 times the 15th term, then the 25th term is:
a) 25 times the 25th term
b) zero
c) 1
d) 2
Solution:
To solve this problem, we need to use the formula for the nth term of an arithmetic progression (AP):
a + (n - 1)d
where:
- a is the first term of the AP
- n is the position of the term
- d is the common difference between consecutive terms
Step 1:
Let's assume that the first term of the AP is 'a' and the common difference is 'd'.
Step 2:
The 10th term of the AP can be expressed as:
a + 9d
Step 3:
The 15th term of the AP can be expressed as:
a + 14d
Step 4:
According to the given information, 10 times the 10th term is equal to 15 times the 15th term:
10(a + 9d) = 15(a + 14d)
Step 5:
Simplifying the equation:
10a + 90d = 15a + 210d
Step 6:
Bringing like terms together:
5a = 120d
Step 7:
Dividing both sides of the equation by 5:
a = 24d
Step 8:
Now we can find the 25th term of the AP using the formula:
a + (n - 1)d
Step 9:
Substituting the values of a and d:
(24d) + (25 - 1)d
Step 10:
Simplifying the expression:
24d + 24d = 48d
Step 11:
Therefore, the 25th term of the AP is 48d.
Conclusion:
The 25th term of the AP is not zero or any multiple of the 25th term. It is equal to 48 times the common difference (48d). Hence, the correct answer is option 'B' - zero.
If the 10 times of the 10th term of an AP is equal to 15 times the 15th term, then the 25th term is:
a) 25 times the 25th term
b) zero
c) 1
d) 2
Solution:
To solve this problem, we need to use the formula for the nth term of an arithmetic progression (AP):
a + (n - 1)d
where:
- a is the first term of the AP
- n is the position of the term
- d is the common difference between consecutive terms
Step 1:
Let's assume that the first term of the AP is 'a' and the common difference is 'd'.
Step 2:
The 10th term of the AP can be expressed as:
a + 9d
Step 3:
The 15th term of the AP can be expressed as:
a + 14d
Step 4:
According to the given information, 10 times the 10th term is equal to 15 times the 15th term:
10(a + 9d) = 15(a + 14d)
Step 5:
Simplifying the equation:
10a + 90d = 15a + 210d
Step 6:
Bringing like terms together:
5a = 120d
Step 7:
Dividing both sides of the equation by 5:
a = 24d
Step 8:
Now we can find the 25th term of the AP using the formula:
a + (n - 1)d
Step 9:
Substituting the values of a and d:
(24d) + (25 - 1)d
Step 10:
Simplifying the expression:
24d + 24d = 48d
Step 11:
Therefore, the 25th term of the AP is 48d.
Conclusion:
The 25th term of the AP is not zero or any multiple of the 25th term. It is equal to 48 times the common difference (48d). Hence, the correct answer is option 'B' - zero.
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Community Answer
If the 10 times of the 10thterm of an AP is equal to 15 times to the 1...
Given (10*A10)=(15*A15)10*(a+9d)=15*(a+14d)10a+90d=15a+210dsend all towards right side5a+120d=05*(a+24d)=0(a+24d=0)a+24d=A25THEREFORE 25th term is zero(0)here d implies common differencea implies first term of APA(n) implies Nth term
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If the 10 times of the 10thterm of an AP is equal to 15 times to the 15th term, then the 25th term is:a)25 times of 25thtermb)zeroc)1d)2Correct answer is option 'B'. Can you explain this answer? 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 10thterm of an AP is equal to 15 times to the 15th term, then the 25th term is:a)25 times of 25thtermb)zeroc)1d)2Correct answer is option 'B'. Can you explain this answer? 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 10thterm of an AP is equal to 15 times to the 15th term, then the 25th term is:a)25 times of 25thtermb)zeroc)1d)2Correct answer is option 'B'. Can you explain this answer?.
If the 10 times of the 10thterm of an AP is equal to 15 times to the 15th term, then the 25th term is:a)25 times of 25thtermb)zeroc)1d)2Correct answer is option 'B'. Can you explain this answer? 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 10thterm of an AP is equal to 15 times to the 15th term, then the 25th term is:a)25 times of 25thtermb)zeroc)1d)2Correct answer is option 'B'. Can you explain this answer? 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 10thterm of an AP is equal to 15 times to the 15th term, then the 25th term is:a)25 times of 25thtermb)zeroc)1d)2Correct answer is option 'B'. Can you explain this answer?.
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