Answer :
the first term is 2 and the 20th term is 1048576 .
Step-by-step explanation:
Here we have , If the sum of the first 12 terms of a geometric series is 8190 and the common ratio is 2. We need to Find the first term and the 20th term. Let's find out:
We know that Sum of a GP is :
⇒ [tex]S_n = \frac{a(r^n-1)}{r-1}[/tex]
So ,Sum of first 12 terms is :
⇒ [tex]S_1_2 = \frac{a(2^{12}-1)}{2-1}[/tex]
⇒ [tex]8190=a(2^{12}-1)[/tex]
⇒ [tex]\frac{8190}{4095}=a[/tex]
⇒ [tex]a=2[/tex]
Now , nth term of a GP is
⇒ [tex]a_n = ar^{n-1}[/tex]
So , 20th term is :
⇒ [tex]a_2_0 = 2(2)^{20-1}[/tex]
⇒ [tex]a_2_0 = (2)^{20}[/tex]
⇒ [tex]a_2_0 = 1048576[/tex]
Therefore , the first term is 2 and the 20th term is 1048576 .