Given a,a1,a2+2a1, a=0, are respectively the 3rd, 4th, and 5th terms of a geometric sequence with ratio r=1. The product of the first five terms of the geometric sequence is....
Explanation
Given u3=a, u4=a1 and u5=a2+2a1 with a=0 and ratio r=1. Then the value of one term with another consecutive term must not be the same.
u3u4=u4u5
u4⋅u4=u3⋅u5
a1⋅a1=a⋅a2+2a1
a21=a(a+2)a
a21=a+21
a2=a+2
a2−a−2=0
Factorize
(a+1)(a−2)=0
a=−1∪a=2
For a=−1
u3=a=−1
u4=a1=−11=−1
Because u3=u4 then its ratio is 1. Whereas the condition is r=1. So a=−1 does not satisfy.
