Q5 of 110 Page 48

Which term of the geometric sequence,

(i) 5, 2, … , is (ii) 1, 2, 4, 8,…, is 1024 ?

(i) a1 = 5, a2 = 2




∵ an = a1rn-1 (n = no. of term, a1 = first term of G.P, r = common ratio)





⇒ n-1 = 7


⇒ n = 8



(ii) a1 = 1, a2 = 2





∵ an = a1rn-1 (n = no. of term, a1 = first term of G.P, r = common ratio)


⇒1024 = 1 × 2n-1


⇒ 210 = 2n-1


⇒ n-1 = 10


⇒ n = 11


∴ 1024 is the 11th term of G.P.


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