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Find the sum of first 25 terms of an AP whose nth term is 1-4n?
Most Upvoted Answer
Find the sum of first 25 terms of an AP whose nth term is 1-4n?
For calculating the sum of 25 term of an AP we have to find
1st term and 25th term .
Hence => 1st term = 1- 4(1) = -3
Similarly 25th term = 1-4(25) = -99
Now,
Sum of 25 term = 25/2 ( 1st term + 25th term)
=> 25/2 ( -102)
=> 25× -51
=> -1275 ..
That's all
1st term and 25th term .
Hence => 1st term = 1- 4(1) = -3
Similarly 25th term = 1-4(25) = -99
Now,
Sum of 25 term = 25/2 ( 1st term + 25th term)
=> 25/2 ( -102)
=> 25× -51
=> -1275 ..
That's all
Community Answer
Find the sum of first 25 terms of an AP whose nth term is 1-4n?
Sum of first 25 terms of an AP
An arithmetic progression (AP) is a sequence of numbers in which each term is obtained by adding a constant difference to the preceding term. In this problem, we are given an AP whose nth term is 1-4n. We need to find the sum of the first 25 terms of this AP.
Finding the common difference
To find the common difference of the given AP, we need to subtract the (n-1)th term from the nth term.
nth term = 1-4n
(n-1)th term = 1-4(n-1) = 5-4n
Common difference = nth term - (n-1)th term
Common difference = (1-4n) - (5-4n) = -4
Finding the sum of the first 25 terms
To find the sum of the first 25 terms, we can use the formula:
Sum of n terms = (n/2) x [2a + (n-1)d]
where a is the first term, d is the common difference and n is the number of terms.
Here, a = 1, d = -4 and n = 25.
Sum of 25 terms = (25/2) x [2(1) + (25-1)(-4)]
Sum of 25 terms = (25/2) x [-96]
Sum of 25 terms = -1200
Final answer
The sum of the first 25 terms of the given AP is -1200.
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Find the sum of first 25 terms of an AP whose nth term is 1-4n? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the sum of first 25 terms of an AP whose nth term is 1-4n? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the sum of first 25 terms of an AP whose nth term is 1-4n?.
Find the sum of first 25 terms of an AP whose nth term is 1-4n? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the sum of first 25 terms of an AP whose nth term is 1-4n? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the sum of first 25 terms of an AP whose nth term is 1-4n?.
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