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For the given Arithmetic progression find the position of first negative term? 50, 47, 44, 41,............
- a)17
- b)18
- c)20
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
For the given Arithmetic progression find the position of first negati...
Let nth term=0, the next term would be first negative term.
0 = 50 + (n - 1) – 3, n = 17.66.. therefore at n = 18 the first negative term would occur.
0 = 50 + (n - 1) – 3, n = 17.66.. therefore at n = 18 the first negative term would occur.
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For the given Arithmetic progression find the position of first negati...
Arithmetic Progression (AP)
An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference.
Given Arithmetic Progression
The given arithmetic progression is:
50, 47, 44, 41, ...
Finding the First Negative Term
To find the position of the first negative term in the given arithmetic progression, we need to determine when the terms start becoming negative.
Using the Formula
We can use the formula for the nth term of an arithmetic progression to find the position of the first negative term.
The formula for the nth term of an arithmetic progression is:
an = a1 + (n - 1)d
Where:
an is the nth term,
a1 is the first term, and
d is the common difference.
Applying the Formula
In the given arithmetic progression, the first term (a1) is 50 and the common difference (d) is -3 (since the progression is decreasing by 3 each time).
Let's substitute these values into the formula and solve for n when the term becomes negative.
an = a1 + (n - 1)d
-3n = 50 + (n - 1)(-3)
-3n = 50 - 3n + 3
-3n + 3n = 50 + 3
0 = 53
Since the equation above is not true, we can conclude that there is no value of n for which the term becomes negative.
Conclusion
Based on the calculations, we can conclude that there is no negative term in the given arithmetic progression. Therefore, the correct answer is option 'D' (None of the mentioned).
An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference.
Given Arithmetic Progression
The given arithmetic progression is:
50, 47, 44, 41, ...
Finding the First Negative Term
To find the position of the first negative term in the given arithmetic progression, we need to determine when the terms start becoming negative.
Using the Formula
We can use the formula for the nth term of an arithmetic progression to find the position of the first negative term.
The formula for the nth term of an arithmetic progression is:
an = a1 + (n - 1)d
Where:
an is the nth term,
a1 is the first term, and
d is the common difference.
Applying the Formula
In the given arithmetic progression, the first term (a1) is 50 and the common difference (d) is -3 (since the progression is decreasing by 3 each time).
Let's substitute these values into the formula and solve for n when the term becomes negative.
an = a1 + (n - 1)d
-3n = 50 + (n - 1)(-3)
-3n = 50 - 3n + 3
-3n + 3n = 50 + 3
0 = 53
Since the equation above is not true, we can conclude that there is no value of n for which the term becomes negative.
Conclusion
Based on the calculations, we can conclude that there is no negative term in the given arithmetic progression. Therefore, the correct answer is option 'D' (None of the mentioned).
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