11th
5 10 20 40 80 160 320 640 1280 2560 5120
From geometric progression,
Gn =G_1 r^(n-1).............................1
but Gn = 5120 G1 = 5 r = 10÷5 =2
5120 = 5 * 2^(n-1)
2^(n-1) = 5120\5 = 1024 = 2^(10)
i.e. n - 1 = 10
so n = 11
so it is 11th term.
Given the geometric progression: a 1 = 5 a 2 = 5 x 2 = 10 a 3 = 10 x 2 = 20 or a 1 x 2^2 = 5 x 4 = 20 Then, we can write: a n = a1 x 2 ^(n - 1) being n the term of the progression Then, an = 5120 = 5 x 2 ^(n-1) Solving this equation For n= 11 , 2 ^10 = 1024 , 1024 x 5 = 5120 The term is n= 11
Clearly: The common ration = 10 / 5 = 2. therefore, a = 5; r = 2; As, we know,
a*r^n-1=5120 :5*2^n-1 = 5120 :2^n-1 = 1024 :2^n-1 = 2^ 10 : n - 1= 10 n = 11
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