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If the nth term of AP is m and the nth term of the same AP is m, then (m + n)th term of AP is
- a)m+n
- b)0
- c)m-n
- d)-m+n
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the nth term of AP is m and the nth term of the same AP is m, then ...
Tn = m = a + (n - l ) d
Tm = n= a + (m - l ) d
subtracting them we get d=-1
and a=m+n-1
Add the two and solve through the options given.
then (m + n)th term of AP= a+(m+n-1)d
= m+n-1+(m+n-1)x-1
= 0
Tm = n= a + (m - l ) d
subtracting them we get d=-1
and a=m+n-1
Add the two and solve through the options given.
then (m + n)th term of AP= a+(m+n-1)d
= m+n-1+(m+n-1)x-1
= 0
Most Upvoted Answer
If the nth term of AP is m and the nth term of the same AP is m, then ...
Tn = p = a + (n - l ) d
Tm = q = a + (m - l ) d
Add the two and solve through the options given.
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Community Answer
If the nth term of AP is m and the nth term of the same AP is m, then ...
Explanation:
Let the common difference be d.
The nth term of the AP is given by:
a + (n-1)d = p
The mth term of the AP is given by:
a + (m-1)d = q
Adding the two equations, we get:
2a + (n+m-2)d = p+q
Solving for the (m+n)th term:
a + (m+n-2)d = (p+q)/2
Using the formula for the nth term, we get:
(m+n-2)d = p - a + q - a
d = (p+q - 2a)/(m+n-2)
Substituting the value of d in the formula for the (m+n)th term, we get:
a + (m+n-2)((p+q - 2a)/(m+n-2)) = a + p + q - 2a
= p + q - a
Therefore, the (m+n)th term of the AP is p + q - a. Thus, option B is correct.
Let the common difference be d.
The nth term of the AP is given by:
a + (n-1)d = p
The mth term of the AP is given by:
a + (m-1)d = q
Adding the two equations, we get:
2a + (n+m-2)d = p+q
Solving for the (m+n)th term:
a + (m+n-2)d = (p+q)/2
Using the formula for the nth term, we get:
(m+n-2)d = p - a + q - a
d = (p+q - 2a)/(m+n-2)
Substituting the value of d in the formula for the (m+n)th term, we get:
a + (m+n-2)((p+q - 2a)/(m+n-2)) = a + p + q - 2a
= p + q - a
Therefore, the (m+n)th term of the AP is p + q - a. Thus, option B is correct.
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If the nth term of AP is m and the nth term of the same AP is m, then (m + n)th term of AP isa)m+nb)0c)m-nd)-m+nCorrect answer is option 'B'. Can you explain this answer?
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