Evaluate the given expression and show the steps, please.

Question

asked Jan 12, 2024 122k views

2 Answers

Chris Woolum · Answer 1 · 2024-01-15T14:45:56+0000

To find:-

Answer:-

We need to evaluate,

$\implies s_4=\displaystyle \sum_(n=1)^(4) 2(3^(n - 1))$

Substituting n = 1 , 2 , 3 and 4 in
2(3^(n - 1)) and then adding them , we have;

$\implies s_4 = 2(3^(1-1)) + 2( 3^(2-1))+2(3^(3-1))+2(3^(4-1)) \\$

Take out 2 as common,

$\implies s_4 = 2 [ 3^0 + 3^1 + 3^2 + 3^3]\\$

$\implies s_4 = 2 [ 1 + 3 + 9 + 27 ] \\$

$\implies s_4 = 2 ( 40) \\$

$\implies \underline{\underline{ s_4 = 80}} \\$

Hence the required answer is 80 .

and we are done!