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Find the sum of first 25 terms of an arithmetic progression whose nth term is given by 7 - 3n.
- a)800
- b)-800
- c)400
- d)-400
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Find the sum of first 25 terms of an arithmetic progression whose nth ...
Understanding the Arithmetic Progression (AP)
The nth term of the arithmetic progression is given by the formula:
- T(n) = 7 - 3n
This indicates that the first term (T(1)) and the common difference (d) can be identified.
Finding the First Term and Common Difference
- First term (T(1)):
- T(1) = 7 - 3(1) = 7 - 3 = 4
- Common difference (d):
- T(2) = 7 - 3(2) = 7 - 6 = 1
- d = T(2) - T(1) = 1 - 4 = -3
Thus, the first term is 4 and the common difference is -3.
Formula for the Sum of the First n Terms
The sum of the first n terms (S(n)) of an AP can be calculated using the formula:
- S(n) = n/2 * (2a + (n - 1)d)
Where:
- n = number of terms (25 in this case)
- a = first term (4)
- d = common difference (-3)
Calculating the Sum of the First 25 Terms
- Substitute the values into the formula:
S(25) = 25/2 * (2(4) + (25 - 1)(-3))
- Simplifying further:
S(25) = 25/2 * (8 - 72)
S(25) = 25/2 * (-64)
S(25) = 25 * (-32)
S(25) = -800
Conclusion
The sum of the first 25 terms of the arithmetic progression is -800, which corresponds to option 'B'.
The nth term of the arithmetic progression is given by the formula:
- T(n) = 7 - 3n
This indicates that the first term (T(1)) and the common difference (d) can be identified.
Finding the First Term and Common Difference
- First term (T(1)):
- T(1) = 7 - 3(1) = 7 - 3 = 4
- Common difference (d):
- T(2) = 7 - 3(2) = 7 - 6 = 1
- d = T(2) - T(1) = 1 - 4 = -3
Thus, the first term is 4 and the common difference is -3.
Formula for the Sum of the First n Terms
The sum of the first n terms (S(n)) of an AP can be calculated using the formula:
- S(n) = n/2 * (2a + (n - 1)d)
Where:
- n = number of terms (25 in this case)
- a = first term (4)
- d = common difference (-3)
Calculating the Sum of the First 25 Terms
- Substitute the values into the formula:
S(25) = 25/2 * (2(4) + (25 - 1)(-3))
- Simplifying further:
S(25) = 25/2 * (8 - 72)
S(25) = 25/2 * (-64)
S(25) = 25 * (-32)
S(25) = -800
Conclusion
The sum of the first 25 terms of the arithmetic progression is -800, which corresponds to option 'B'.
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Community Answer
Find the sum of first 25 terms of an arithmetic progression whose nth ...
tn = 7 - 3n
t1 = 7 - 3 × 1 = 4 ⇒ a = 4
t2 = 7 - 3 × 2 = 1
d = 1 - 4 = -3
t1 = 7 - 3 × 1 = 4 ⇒ a = 4
t2 = 7 - 3 × 2 = 1
d = 1 - 4 = -3
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Find the sum of first 25 terms of an arithmetic progression whose nth term is given by 7 - 3n.a)800b)-800c)400d)-400Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 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 arithmetic progression whose nth term is given by 7 - 3n.a)800b)-800c)400d)-400Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the sum of first 25 terms of an arithmetic progression whose nth term is given by 7 - 3n.a)800b)-800c)400d)-400Correct answer is option 'B'. Can you explain this answer?.
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