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If 7th and 13th terms of an A.P. be 34 and 64, respectively, then it's 18th term is :
- a)87
- b)88
- c)89
- d)90
Correct answer is option 'C'. Can you explain this answer?
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If 7thand 13thterms of an A.P. be 34 and 64, respectively, then its 18...
To find the 18th term of an arithmetic progression (A.P.), we need to determine the common difference (d) first.
Given information:
- The 7th term of the A.P. is 34.
- The 13th term of the A.P. is 64.
Finding the common difference (d):
The formula to find the nth term of an A.P. is given by:
an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
Using the 7th term (a7 = 34) and the 13th term (a13 = 64), we can set up two equations:
a7 = a1 + 6d
a13 = a1 + 12d
Subtracting the first equation from the second equation:
a13 - a7 = (a1 + 12d) - (a1 + 6d)
64 - 34 = 12d - 6d
30 = 6d
d = 30/6
d = 5
Therefore, the common difference (d) of the A.P. is 5.
Finding the 18th term (a18):
Now that we know the common difference (d = 5), we can find the 18th term using the formula:
a18 = a1 + (18 - 1)d
a18 = a1 + 17d
To determine the value of a1, we can substitute the 7th term (a7 = 34) into the equation:
34 = a1 + 6d
34 = a1 + 6(5)
34 = a1 + 30
a1 = 34 - 30
a1 = 4
Now we can substitute the values of a1 and d into the equation for the 18th term:
a18 = 4 + 17(5)
a18 = 4 + 85
a18 = 89
Therefore, the 18th term of the arithmetic progression is 89, which corresponds to option C.
Given information:
- The 7th term of the A.P. is 34.
- The 13th term of the A.P. is 64.
Finding the common difference (d):
The formula to find the nth term of an A.P. is given by:
an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
Using the 7th term (a7 = 34) and the 13th term (a13 = 64), we can set up two equations:
a7 = a1 + 6d
a13 = a1 + 12d
Subtracting the first equation from the second equation:
a13 - a7 = (a1 + 12d) - (a1 + 6d)
64 - 34 = 12d - 6d
30 = 6d
d = 30/6
d = 5
Therefore, the common difference (d) of the A.P. is 5.
Finding the 18th term (a18):
Now that we know the common difference (d = 5), we can find the 18th term using the formula:
a18 = a1 + (18 - 1)d
a18 = a1 + 17d
To determine the value of a1, we can substitute the 7th term (a7 = 34) into the equation:
34 = a1 + 6d
34 = a1 + 6(5)
34 = a1 + 30
a1 = 34 - 30
a1 = 4
Now we can substitute the values of a1 and d into the equation for the 18th term:
a18 = 4 + 17(5)
a18 = 4 + 85
a18 = 89
Therefore, the 18th term of the arithmetic progression is 89, which corresponds to option C.
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If 7thand 13thterms of an A.P. be 34 and 64, respectively, then its 18thterm is :a)87b)88c)89d)90Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 7thand 13thterms of an A.P. be 34 and 64, respectively, then its 18thterm is :a)87b)88c)89d)90Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 7thand 13thterms of an A.P. be 34 and 64, respectively, then its 18thterm is :a)87b)88c)89d)90Correct answer is option 'C'. Can you explain this answer?.
If 7thand 13thterms of an A.P. be 34 and 64, respectively, then its 18thterm is :a)87b)88c)89d)90Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 7thand 13thterms of an A.P. be 34 and 64, respectively, then its 18thterm is :a)87b)88c)89d)90Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 7thand 13thterms of an A.P. be 34 and 64, respectively, then its 18thterm is :a)87b)88c)89d)90Correct answer is option 'C'. Can you explain this answer?.
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