Question
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
ernesto
please show how to solve the problem...
Annora Beatrice Monrrow
Um... i'm sorry as soon as I say this I was completely lost- sorry!!!!!!
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