If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.*
Answers
Answer:
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Step-by-step explanation:
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If 7 times the seventh term of the AP is equal to 5 times the fifth term, then the value of its 12th term = 0
Given:
7 times the seventh term of the AP is equal to 5 times the fifth term
To find:
The value of 12th term of this AP series
Solution:
The general term of an AP series is given as:
an = a + (n -1)*d
Using this formula,
the seventh term of the AP is given as:
a7 = a + (7 -1)*d
=> a7 = a + 6*d
and
the fifth term of the AP is given as:
a5 = a + (5 -1)*d
=> a5 = a + 4*d
It is given that 7 times the seventh term of the AP is equal to 5 times the fifth term
=> 7*a7 =5*a5
=> 7*(a + 6*d) = 5*(a + 4*d)
=> 7*a + 7*6*d = 5*a + 5*4*d
=> 7*a - 5*a = 5*4*d - 7*6*d
=> 2*a = 20*d - 42*d
=> 2*a = (-22)*d
=> a = (-11)*d
=> a = -11d
The 12th term of the AP is given as:
a12 = a + (12 -1)*d
=> a12 = a + 11*d ---(1)
Substituting the value of a from equation (1) in this equation, we get
a12 = (-11)*d + 11*d
=> a12 = 0
Hence,
the value of 12th term of the AP = 0
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