NDA2011MathematicsSequences and SeriesActual

If the 10^ th term of a GP is 9 and 4^ th term is 4 , then what is its 7^ th term?

Options

A6
B14
C27/14
D56/15

Correct answer

A. 6

Step-by-step solution

Let first term of G.P. is a and common ratio =r 10^ th term of G.P. is 9 a r^9=9 ...(i) and a r^3=4 (ii) Divide (i) by (ii) a r^9 a r^3 = 9 4 r^6= 9 4 (r^3 )^2= ( 3 2 )^2r^3= 3 2 Putting the value of r^3 in (i) a r^3=4a ( 3 2 )=4 a= 8 3 7^ th term =a r^6= 8 3 9 4 =6 .

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