Answer:
Number of terms: n=6
Step-by-step explanation:
We are given:
a₁ = 0.75
r = 4
Sₙ = 1023.75
We need to find number of terms i.e n
The formula used will be:[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
Putting values and fining n
[tex]S_n=\frac{a(r^n-1)}{r-1}\\1023.75=\frac{0.75(4^n-1)}{4-1}\\ 1023.75=\frac{0.75(4^n-1)}{3}\\3\times 1023.75=0.75(4^n-1)\\3071.25=0.75(4^n-1)\\4^n-1=\frac{3071.25}{0.75}\\4^n-1=4095\\4^n=4095+1\\4^n=4096[/tex]
We know that [tex]4^6= 4096[/tex]
[tex]4^n=4^6[/tex]
Using Exponent rule: [tex]a^n=a^b => n=b[/tex]
[tex]n=6[/tex]
So, Number of terms: n=6
