Answer: 1456
Explanation:
For this problem, there is a short cut you can use to solve it. In order to understand the meaning of summation, I will do it the long way to show how a summation works. This sum is from n=1 to n=6. We plug in the values of n into the expression, then add together the sums.
n=1
4(3)¹⁻¹
=4(3)⁰
=4
-------------------------------------------------------------------
n=2
4(3)²⁻¹
=4(3)¹
=12
-------------------------------------------------------------------
n=3
4(3)³⁻¹
=4(3)²
=4(9)
=36
-------------------------------------------------------------------
n=4
4(3)⁴⁻¹
=4(3)³
=4(27)
=108
-------------------------------------------------------------------
n=5
4(3)⁵⁻¹
=4(3)⁴
=4(81)
=324
-------------------------------------------------------------------
n=6
4(3)⁶⁻¹
=4(3)⁵
=4(243)
=972
-------------------------------------------------------------------
Now that we have all our values, we can add them together to get the sum.
4+12+36+108+324+972=1456
The sum is 1456. You can also notice that the values multiply by 3 each time.