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The 3rd term of arithmetic progression is 7 and the 7 term is 15.find the comman difference and the first term.?
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The 3rd term of arithmetic progression is 7 and the 7 term is 15.find ...
Given information:
- 3rd term (a3) = 7
- 7th term (a7) = 15
Finding the common difference (d):
- Using the formula for the nth term of an arithmetic progression: an = a1 + (n-1)d
- Substituting the given values, we get:
a3 = a1 + 2d (since n=3)
a7 = a1 + 6d (since n=7)
- From the given data, we have a3 = 7 and a7 = 15
- Substituting these values, we get:
7 = a1 + 2d
15 = a1 + 6d
- Subtracting the first equation from the second, we get:
15 - 7 = 6d - 2d
8 = 4d
d = 2
Finding the first term (a1):
- Using the formula for the nth term of an arithmetic progression: an = a1 + (n-1)d
- Substituting the values of a3 and d, we get:
7 = a1 + 2(2)
7 = a1 + 4
a1 = 3
Conclusion:
- The common difference (d) is 2
- The first term (a1) is 3.
- 3rd term (a3) = 7
- 7th term (a7) = 15
Finding the common difference (d):
- Using the formula for the nth term of an arithmetic progression: an = a1 + (n-1)d
- Substituting the given values, we get:
a3 = a1 + 2d (since n=3)
a7 = a1 + 6d (since n=7)
- From the given data, we have a3 = 7 and a7 = 15
- Substituting these values, we get:
7 = a1 + 2d
15 = a1 + 6d
- Subtracting the first equation from the second, we get:
15 - 7 = 6d - 2d
8 = 4d
d = 2
Finding the first term (a1):
- Using the formula for the nth term of an arithmetic progression: an = a1 + (n-1)d
- Substituting the values of a3 and d, we get:
7 = a1 + 2(2)
7 = a1 + 4
a1 = 3
Conclusion:
- The common difference (d) is 2
- The first term (a1) is 3.
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The 3rd term of arithmetic progression is 7 and the 7 term is 15.find the comman difference and the first term.?
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The 3rd term of arithmetic progression is 7 and the 7 term is 15.find the comman difference and the first term.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The 3rd term of arithmetic progression is 7 and the 7 term is 15.find the comman difference and the first term.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The 3rd term of arithmetic progression is 7 and the 7 term is 15.find the comman difference and the first term.?.
The 3rd term of arithmetic progression is 7 and the 7 term is 15.find the comman difference and the first term.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The 3rd term of arithmetic progression is 7 and the 7 term is 15.find the comman difference and the first term.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The 3rd term of arithmetic progression is 7 and the 7 term is 15.find the comman difference and the first term.?.
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