Question

Determine the number of terms n in each geometric series. 13) a1 = 0.75, r = 4, Sn =1023.75

Answer 1

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:$S_n=\frac{a(r^n-1)}{r-1}$

Putting values and fining n

$S_n=\frac{a(r^n-1)}{r-1}\\1023.75=\frac{0.75(4^n-1)}{4-1}\\ 1023.75=\frac{0.75(4^n-1)}{3}\\3\times 1023.75=0.75(4^n-1)\\3071.25=0.75(4^n-1)\\4^n-1=\frac{3071.25}{0.75}\\4^n-1=4095\\4^n=4095+1\\4^n=4096$

We know that $4^6= 4096$

$4^n=4^6$

Using Exponent rule: $a^n=a^b => n=b$

$n=6$

So, Number of terms: n=6