math
posted by saraah on .
in a geometric sequence the first term is 2. The 3rd term is the sum of the 1st and 2nd term. Find the ratio, and the 2 terms

a = 2
term(3) = ar^2 = 2r^2
term(2) = ar = 2r
2 + 2r = 2r^2
r^2  r  1 = 0
r = (1 ± √5)/2
if r = (1 + √5)/2 , which btw, is the GOLDEN RATIO
the first 2 terms are
2 and 1 + √5
if r = (1  √5)/2
the first 2 terms are
2 and 1  √5
check: using my calculator and decimals
terms are 2 , 3.236.. , 5.236..
the third time is the sum of the first two
or
terms are 2, 1.236.. , .7639...
.7639 = 2  1.236 , ok