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?
3 answers
please show how to solve the problem...
Um... i'm sorry as soon as I say this I was completely lost- sorry!!!!!!
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