Question:
if 5 times the 5th term of an A.P. is equal to 7 times the 7th term find its 25th term
Answer:
The correct question is:
if 5 times the 5th term of an A.P. is equal to 7 times the 7th term finds its 12th term.
Solution:
Let a is the first term and d is the common difference of the AP.
Given, 5 times the 5th term of an A.P. is equal to 7 times the 7th term
=> 5 * T5 = 7 * T7
=> 5{a + (5 - 1)d} = 7{a + (7 - 1)d}
=> 5(a + 4d) = 7(a + 6d)
=> 5a + 20d = 7a + 42d
=> 7a + 42d - 5a - 20d = 0
=> 2a + 22d = 0
=> 2(a + 11)d = 0
=> a + 11d = 0
=> a + (12 - 1)d = 0
=> T12 = 0
So, 12th term of the given AP is zero.
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