If the second term of a GP is 6 and the fourth term is 54 find the nth term
a r = 6
a r^3 = 54
dividing equations ... r^2 = 3 ... a = 2
nth term ... 2 * 3^(n - 1)
small slip-up
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r^2 = 9
r = ± 3,
if r = 3, a = 2 , then sequence is 2, 6, 18, .... , term(n) = 2*3^(n-1)
if r = -3, a = -2, then the sequence is -2, 6, -18, ....,
term(n) = (-1)^(n+1)*2*3^(n-1)