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If in an arithmetic progression, the sth term is 2t, and the tth term is 2s, then what is |d|, where d the common difference of the arithmetic progression?
Correct answer is '2'. Can you explain this answer?
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If in an arithmetic progression, the sth term is 2t, and the tthterm i...
We know that, the sth term of the AP is 21 and the tth term is 2s.
Let the first term of the AP be a and the common difference be d.
Ts = a + (s - 1)d = 2t ...(i)
Tt = a + (t - 1)d = 2s ...(ii)
Subtracting equation (i) from equation (ii), we get,
(t- 1 - s+ 1)d = 2s-2t
(t - s)d = -2(s - t)
(f - s)d = -2(t - s)
d = -2
|d| = 2
Answer: 2
Let the first term of the AP be a and the common difference be d.
Ts = a + (s - 1)d = 2t ...(i)
Tt = a + (t - 1)d = 2s ...(ii)
Subtracting equation (i) from equation (ii), we get,
(t- 1 - s+ 1)d = 2s-2t
(t - s)d = -2(s - t)
(f - s)d = -2(t - s)
d = -2
|d| = 2
Answer: 2
Most Upvoted Answer
If in an arithmetic progression, the sth term is 2t, and the tthterm i...
Understanding the Arithmetic Progression
In an arithmetic progression, each term is obtained by adding a constant difference, denoted as 'd', to the previous term. For example, if the first term is 'a', the second term is 'a + d', the third term is 'a + 2d', and so on.
Given Information
We are given that the 's'th term of the arithmetic progression is 2t, and the 't'th term is 2s.
First Step: Finding the 's'th term
To find the 's'th term, we can substitute 's' in place of 't' in the equation for the 't'th term.
Substituting 's' for 't' in the equation 2s = a + (t-1)d, we get:
2s = a + (s-1)d
This equation represents the 's'th term of the arithmetic progression.
Second Step: Finding the 't'th term
To find the 't'th term, we can substitute 't' in place of 's' in the equation for the 's'th term.
Substituting 't' for 's' in the equation 2t = a + (s-1)d, we get:
2t = a + (t-1)d
This equation represents the 't'th term of the arithmetic progression.
Using the Given Information
From the given information, we have the following equations:
2s = a + (s-1)d (Equation 1)
2t = a + (t-1)d (Equation 2)
Substituting '2s' for 'a' in Equation 2
Substituting '2s' for 'a' in Equation 2, we get:
2t = 2s + (t-1)d
Simplifying this equation, we get:
2t = 2s + td - d
2t = 2s + (t-1)d
Comparing this equation with Equation 2, we see that they are identical.
Conclusion: Finding the Common Difference
Since Equation 2 is satisfied by Equation 1, we can conclude that the common difference 'd' is equal to 1.
However, the given answer states that the value of |d| is 2. This implies that the common difference 'd' can also be -2.
Therefore, the correct answer is that |d| can be either 1 or 2, depending on the specific values of 's' and 't' in the arithmetic progression.
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If in an arithmetic progression, the sth term is 2t, and the tthterm is 2s, then what is |d|, where d the common difference of the arithmetic progression?Correct answer is '2'. Can you explain this answer?
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