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In an AP the first and last terms are 7 and 73 respectively if the sum of all its term is 480 then the number of the terms of an AP is?
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In an AP the first and last terms are 7 and 73 respectively if the sum...
Understanding the Problem
To find the number of terms in an arithmetic progression (AP) where the first term (a) is 7, the last term (l) is 73, and the sum of the terms (S) is 480, we can use the properties of AP.
Formulas to Use
- Sum of AP: The sum of the first n terms of an AP can be expressed as:
\[ S = \frac{n}{2} \times (a + l) \]
- Finding n: Rearranging the sum formula gives us:
\[ n = \frac{2S}{a + l} \]
Substituting Values
1. Given values:
- \( a = 7 \)
- \( l = 73 \)
- \( S = 480 \)
2. Calculate \( a + l \):
\[ a + l = 7 + 73 = 80 \]
3. Substituting into the n formula:
\[ n = \frac{2 \times 480}{80} \]
Calculating n
- Perform the multiplication:
\[ n = \frac{960}{80} \]
- Simplify the division:
\[ n = 12 \]
Conclusion
The number of terms in the arithmetic progression is 12.
This means there are 12 terms in the sequence starting from 7 and ending at 73, with a total sum of 480.
To find the number of terms in an arithmetic progression (AP) where the first term (a) is 7, the last term (l) is 73, and the sum of the terms (S) is 480, we can use the properties of AP.
Formulas to Use
- Sum of AP: The sum of the first n terms of an AP can be expressed as:
\[ S = \frac{n}{2} \times (a + l) \]
- Finding n: Rearranging the sum formula gives us:
\[ n = \frac{2S}{a + l} \]
Substituting Values
1. Given values:
- \( a = 7 \)
- \( l = 73 \)
- \( S = 480 \)
2. Calculate \( a + l \):
\[ a + l = 7 + 73 = 80 \]
3. Substituting into the n formula:
\[ n = \frac{2 \times 480}{80} \]
Calculating n
- Perform the multiplication:
\[ n = \frac{960}{80} \]
- Simplify the division:
\[ n = 12 \]
Conclusion
The number of terms in the arithmetic progression is 12.
This means there are 12 terms in the sequence starting from 7 and ending at 73, with a total sum of 480.
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In an AP the first and last terms are 7 and 73 respectively if the sum of all its term is 480 then the number of the terms of an AP is?
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In an AP the first and last terms are 7 and 73 respectively if the sum of all its term is 480 then the number of the terms of an AP is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In an AP the first and last terms are 7 and 73 respectively if the sum of all its term is 480 then the number of the terms of an AP is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an AP the first and last terms are 7 and 73 respectively if the sum of all its term is 480 then the number of the terms of an AP is?.
In an AP the first and last terms are 7 and 73 respectively if the sum of all its term is 480 then the number of the terms of an AP is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In an AP the first and last terms are 7 and 73 respectively if the sum of all its term is 480 then the number of the terms of an AP is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an AP the first and last terms are 7 and 73 respectively if the sum of all its term is 480 then the number of the terms of an AP is?.
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