Let the first three terms 2 , p and q , with q  = 2 , of a G.P. be respectively the 7 th , 8 th and 1 3 th terms of an A.P. If the 5 th term of the G.P. is the n th term of the A.P., then n is equal

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Let the first three terms 2 , p and q , with q  = 2 , of a G.P. be respectively the 7 th , 8 th and 1 3 th terms of an A.P. If the 5 th term of the G.P. is the n th term of the A.P., then n is equal to:

TestHub · Accepted Answer

p 2 = 2 q 2 = a + 6 d ...(i) p = a + 7 d ...(ii) q = a + 12 d ...(iii) p − 2 = d ((ii) - (i)) q − p = 5 d ((iii) - (ii)) q − p = 5 d ​ q − p = 5 ( p − 2 ) q = 6 p − 10 p 2 = 2 ( 6 p − 10 ) p 2 − 12 p + 20 = 0 p = 10 , 2 p = 10 ; q = 50 d = 8 a = − 46 2 , 10 , 50 , 250 , 1250 a 4 = a + ( n − 1 ) d 1250 = − 46 + ( n − 1 ) 8 n = 163 ​

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