Question

find the sum of the series 2+6+18+54+......+4374

Answer 1

a=3
last = 4374=arn-1
Σ= a(rn-1)/(r-1)
=(arn-a )/2
=(arn-1.r-a)/2
=(4374.3-2)/2
= 6560 .

Answer 2

The sum of the series is 6560.

Step-by-step explanation:

The sum of the series 2 + 6 + 18 + 54 +......+ 4374.

Here, first term(a) = 2, common ration(r) = $\dfrac{6}{2} =3$

and $a_{n} =4374$

To find, the sum of the series = ?

$a_{n} =ar^{n-1}$

⇒ $2(3)^{n-1}=4374$

⇒ $(3)^{n-1}=\dfrac{4374}{2} =2187$

⇒ $(3)^{n-1}=3^{7}$

⇒$n-1 =7$

∴$n=7+1=8$

The sum of the series,

$S_{n} =\dfrac{a(r^{n}-1)}{r-1}$

⇒$S_{n} =\dfrac{2(3^{8}-1)}{3-1}$

⇒ $=3^{8}-1=6561-1$

$=6560$

Hence, the sum of the series is 6560.