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If the sum of the first n terms of an arithmetic progression is given by (Sn=3n^2+5n), find and 15th term.?
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If the sum of the first n terms of an arithmetic progression is given ...
Explanation:
Finding the 15th term of an arithmetic progression:
An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. The sum of the first n terms of an arithmetic progression can be calculated using the formula Sn = n/2 [2a + (n-1)d], where a is the first term, d is the common difference, and n is the number of terms.
Given that Sn = 3n^2 + 5n, we can equate this to the formula for the sum of an arithmetic progression:
3n^2 + 5n = n/2 [2a + (n-1)d]
Using the formula for the sum of an AP:
By comparing the coefficients of n^2 and n on both sides, we can find the values of a and d:
3 = d/2
5 = a + d
Solving these two equations simultaneously, we get d = 6 and a = -1.
Substitute the values of a and d:
Now that we have found the values of a and d, we can find the 15th term of the arithmetic progression using the formula for the nth term of an AP:
Tn = a + (n-1)d
T15 = -1 + (15-1)6
T15 = -1 + 84
T15 = 83
Therefore, the 15th term of the arithmetic progression is 83.
Finding the 15th term of an arithmetic progression:
An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. The sum of the first n terms of an arithmetic progression can be calculated using the formula Sn = n/2 [2a + (n-1)d], where a is the first term, d is the common difference, and n is the number of terms.
Given that Sn = 3n^2 + 5n, we can equate this to the formula for the sum of an arithmetic progression:
3n^2 + 5n = n/2 [2a + (n-1)d]
Using the formula for the sum of an AP:
By comparing the coefficients of n^2 and n on both sides, we can find the values of a and d:
3 = d/2
5 = a + d
Solving these two equations simultaneously, we get d = 6 and a = -1.
Substitute the values of a and d:
Now that we have found the values of a and d, we can find the 15th term of the arithmetic progression using the formula for the nth term of an AP:
Tn = a + (n-1)d
T15 = -1 + (15-1)6
T15 = -1 + 84
T15 = 83
Therefore, the 15th term of the arithmetic progression is 83.
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If the sum of the first n terms of an arithmetic progression is given by (Sn=3n^2+5n), find and 15th term.?
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If the sum of the first n terms of an arithmetic progression is given by (Sn=3n^2+5n), find and 15th term.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the sum of the first n terms of an arithmetic progression is given by (Sn=3n^2+5n), find and 15th term.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the first n terms of an arithmetic progression is given by (Sn=3n^2+5n), find and 15th term.?.
If the sum of the first n terms of an arithmetic progression is given by (Sn=3n^2+5n), find and 15th term.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the sum of the first n terms of an arithmetic progression is given by (Sn=3n^2+5n), find and 15th term.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the first n terms of an arithmetic progression is given by (Sn=3n^2+5n), find and 15th term.?.
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