10) Given a,4,8,... is a geometric sequence. Find the value of a and the 10th term and 20th term.

Question

asked Aug 5, 2024 167k views

1 Answer

Parvin Gasimzade · Answer 1 · 2024-08-10T20:10:25+0000

We need to find the formula of the sequence.

The general formula of a geometric sequence is
a_n=ar^(n-1) .

We know that
r=(a_n)/(a_(n-1)) , so
a=(a_2)/(r) .

Therefore
r=(8)/(4)=2 and
a=(4)/(2)=2 .

So
$a_n=2\cdot 2^(n-1)=2^n$ .

Therefore

$a_(10)=2^(10)=1024\\a_(20)=2^(20)=1048576$