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Find the sum of the first 15th term of the arithmetic progression 7 , 11, 15, 19...,?
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Find the sum of the first 15th term of the arithmetic progression 7 , ...
Sum of the First 15 Terms of an Arithmetic Progression
Arithmetic progressions are sequences in which the difference between consecutive terms is constant. In this case, the given arithmetic progression is 7, 11, 15, 19,...
Finding the Common Difference (d)
To find the common difference (d) between the terms, we subtract the second term from the first term:
11 - 7 = 4
Finding the 15th Term (a15)
The formula to find the nth term of an arithmetic progression is:
an = a1 + (n-1)d
Substitute the values:
a15 = 7 + (15-1) * 4
a15 = 7 + 56
a15 = 63
Finding the Sum of the First 15 Terms
The sum of the first n terms of an arithmetic progression can be calculated using the formula:
Sum = n/2 * (2a1 + (n-1)d)
Substitute the values:
Sum = 15/2 * (2*7 + (15-1)*4)
Sum = 7.5 * (14 + 56)
Sum = 7.5 * 70
Sum = 525
Therefore, the sum of the first 15 terms of the arithmetic progression 7, 11, 15, 19,... is 525.
Arithmetic progressions are sequences in which the difference between consecutive terms is constant. In this case, the given arithmetic progression is 7, 11, 15, 19,...
Finding the Common Difference (d)
To find the common difference (d) between the terms, we subtract the second term from the first term:
11 - 7 = 4
Finding the 15th Term (a15)
The formula to find the nth term of an arithmetic progression is:
an = a1 + (n-1)d
Substitute the values:
a15 = 7 + (15-1) * 4
a15 = 7 + 56
a15 = 63
Finding the Sum of the First 15 Terms
The sum of the first n terms of an arithmetic progression can be calculated using the formula:
Sum = n/2 * (2a1 + (n-1)d)
Substitute the values:
Sum = 15/2 * (2*7 + (15-1)*4)
Sum = 7.5 * (14 + 56)
Sum = 7.5 * 70
Sum = 525
Therefore, the sum of the first 15 terms of the arithmetic progression 7, 11, 15, 19,... is 525.
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Find the sum of the first 15th term of the arithmetic progression 7 , 11, 15, 19...,?
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Find the sum of the first 15th term of the arithmetic progression 7 , 11, 15, 19...,? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the sum of the first 15th term of the arithmetic progression 7 , 11, 15, 19...,? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the sum of the first 15th term of the arithmetic progression 7 , 11, 15, 19...,?.
Find the sum of the first 15th term of the arithmetic progression 7 , 11, 15, 19...,? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the sum of the first 15th term of the arithmetic progression 7 , 11, 15, 19...,? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the sum of the first 15th term of the arithmetic progression 7 , 11, 15, 19...,?.
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