Question 1181531
a1= 120 first
common ratio = 1/5 ( ratio of consecutive terms)
last term = 24/78125

an = a1*r^(n-1)

24/78125 = 120*(1/5)^(n-1)

(1/5)^(n-1) = 1/390625


(n-1) log (1/5) = log(1/390625)

n-1=8
n=9 the number of terms



2-(4/3) +(8/9)-(16/27) ....

=> (2+(8/9) .....) - ((4/3) +16/27) ....)

Use the sum of n terms formula for both and simplify