Show work and explain with formulas.26. Find the sum of the first 6 terms of a geometric series: 80 + (-20) + 5 + ...27. Find the 4 geometric means between 1/25 and 125.
Accepted Solution
A:
26)t2/t1=-20/80=-1/4=-0.25t3/t2=5/(-20)=-1/4-0.25 So,common ratio=-1/4The 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) =63.9827)1/25 , ?, ?, ?, ?, 125where '?' means geometric meanYou 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^5125×25=r^5r=65.6631951101=65.66thus,t2=t1×r=65.66/25t3=t2×r=(65.66/25)×65.66 =65.66²/25Similarly,t4=65.66³/25t5=65.66⁴/25t2,t3,t4 and t5 are required geometric means