Question

Find the sum of the first five terms of the geometric series 8, −24, 72, …

484
488
648
684

Answer 1

Answer:

The sum of first five terms are $S_{5} = 8 -24 +72 -216 +648 = 488$

Step-by-step explanation:

Step 1:-

sequence:-  an ordered pair of real numbers is called an sequence

Example:- { 1, 3, 5, 7, 9, ..........}

and it is denoted by <$a_{n}$

series:-

The sum of the sequence is called a series and it is denoted by

$S_{n}$

The gives series is geometric series 8,-24,72,.......

here a=8 and the ratio r=$\frac{a_{2} }{a_{1} }$

$r= -3$

Step 2:-

Find The fourth term of the given sequence

Given a=8 and r= -3

$t_{n}= a r^{n-1}$

$t_{4} = 8(-3)^{4-1}$

$t_{4}=8(-3)^3= -216$

Find The fifth term of the given sequence

Given a=8 and r= -3

$t_{n}=a r^{n-1}$

$t_{5} = 8(-3)^{5-1}$

$t_{5}=8(-3)^4= 648$

Step 3:-

now the geometric sequence  8,-24,72,-216,648

sum of the geometric sequence is called geometric series

The first five terms of geometric series

$S_{5} } = 8 -24+72-216+648=488$

or

By using sum of the Geometric series formula

$S_{n} =\frac{a(1-r^{n}) }{1-r}  if  r < 1$

here a=8 and r = -3 <1

$S_{5} = \frac{8(1-(-3)^5}{1-(-3)} = 488$