Question

If twice the 11th term of an A.P. is equal to 7 times of its 21st term, then its 25th term is equal to [J & K 2005]
A) 24 B) 120 C) 0 D) None of these

Answer 1

n th term of  an Ap = a+(n-1)d

11 th term = a+(11-1)d = a+10d

21 st term= a+(21-1)d= a+20d

given

2(a+10d)= 7(a+20d)

2a+ 20d = 7a +140d

20d-140d= 7a-2a

-120d=5a

a=-120d/5----------------------(1)

25th term = a+24d

                   =  (-120d/5)+24d

                  = (-120d+120d)/5

                  = 0

             

Answer 2

Let a is the first term of AP and d is common difference

∴ 11th term will be a + 10d

21st term will be a + 20d

We need to find 25th term which is a + 24d

Here given that 2 times of 11th term is equals to 7 times the 21st term

2( a + 10d) = 7( a + 20d)

2a + 20d = 7a + 140d

5a + 120d = 0

Or a + 24d =0 (which is 25th term)

∴25th term of given AP = 0