Question

T1+T2=-1 and T3+T4=-4. What are the first three numerical terms of this geometric sequence if r>0?

Answer 1

Geometric progression is a, ar, ar², ar³, ..., where a is the first term T₁, and r is the common ratio.

T₁+T₂=-1, T₃+T₄=-4 so a+ar=-1=a(1+r); ar²+ar³=-4=ar²(1+r).

ar²(1+r)/(a(1+r))=-4/-1=r² so r²=4, r=2 (r>0).

a(1+r)=3a=-1, a=-⅓.

GP=-⅓, -⅔, -1⅓, -2⅔, -5⅓, ... T₁+T₂=-⅓-⅔=-1;  T₃+T₄=-1⅓-2⅔=-4.