Asked by ernesto
if the 3rd,5th and 11th terms are distinct and form a geometric sequence, what is the 2020th term if then 4th term is 5?
Answers
Answered by
ernesto
please show how to solve the problem...
Answered by
Annora Beatrice Monrrow
Um... i'm sorry as soon as I say this I was completely lost- sorry!!!!!!
Answered by
R_scott
a + 3d = 5 ... a = 5 - 3d
(a + 4d) / (a + 2d) = (a + 10d) / (a + 4d) ... "cross" multiply
a^2 + 8ad + 16d^2 = a^2 + 12ad + 20d^2 ... subtract a^2
8ad + 16d^2 = 12ad + 20d^2 ... divide by 2d
4a + 8d = 6a + 10d ... substituting ... 20 - 12d + 8d = 30 - 18d + 10d
solve for d , then substitute back to find a
(a + 4d) / (a + 2d) = (a + 10d) / (a + 4d) ... "cross" multiply
a^2 + 8ad + 16d^2 = a^2 + 12ad + 20d^2 ... subtract a^2
8ad + 16d^2 = 12ad + 20d^2 ... divide by 2d
4a + 8d = 6a + 10d ... substituting ... 20 - 12d + 8d = 30 - 18d + 10d
solve for d , then substitute back to find a
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