Let three positive numbers a, b, c (in order) be in HP such that a+c=8 . If t_n is a geometric progression with common ratio 3 where t₁=a- b 2 , t₂= b 2 and t₃=c- b 2 then find the value of t₇ ( 2 3 )^6 .

Question

Quantrex Academy · Accepted Answer

Correct answer: 32

aligned b & = 2 a c a+c a c=4 b b 2 a-b & =3 b=6 a-3 b 2 b=3 a a c & =2 3 a 6 a=a c c=6, a=2, b=3 t₁ & = 1 2 , t₂= 3 2 , t₃= 9 2 t₇ & = 1 2 3^6 t₇ ( 2 3 )^6=2^5 aligned

Let three positive numbers a, b, c (in order) be in HP such that a+c=8 . If t_n is a geometric progression with common ratio 3 where t₁=a- b 2 , t₂= b 2 and t₃=c- b 2 then find the value of t₇ ( 2 3 )^6 .

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