26)
t2/t1=-20/80=-1/4=-0.25
t3/t2=5/(-20)=-1/4-0.25
So,
common ratio=-1/4
The formula applied to calculate sum of first n terms of a GP:
Sn=a(rⁿ-1)/(r-1)
S6=80{(-0.25)^6-1}/(-0.25-1)
=63.98
27)
1/25 , ?, ?, ?, ?, 125
where '?' means geometric mean
You can find those missing terms in between 1/25 and 125 to get geometric means.
For that we need to find common ratio by using formula,
tn=t1×r^(n-1)
here n=last nth term=6,so,
t6=(1/25)×r^(6-1)
125=(1/25)×r^5
125×25=r^5
r=65.6631951101=65.66
thus,
t2=t1×r=65.66/25
t3=t2×r=(65.66/25)×65.66
=65.66²/25
Similarly,
t4=65.66³/25
t5=65.66⁴/25
t2,t3,t4 and t5 are required geometric means
