Question

Evaluate the summation of 3 times negative 2 to the n minus 1 power, from n equals 1 to 5. A) −93. B) −33. C) 33. D) 93

Answer 1

(C)33

Explanation:

The given summation can be written as:

`\sum_(n=1)^(5)3(-2)^(n-1)`

Putting the values of n from 1 to 5 in the above equation, we get

=
`3(-2)^0+3(-2)^1+3(-2)^2+3(-2)^3+3(-2)4`

=
`3+(-6)+3(4)+3(-8)+3(16)`

=
`3-6+12-24+48`

=
`33`

Thus, the value of the given summation
`\sum_(n=1)^(5)3(-2)^(n-1)` is 33.

Hence, option C is correct.

Answer 2

∑ ( from n = 1 to n =5 ) 3 · ( -2 ) ^( n -1 )
a 1 = 3 · ( -2 ) ^0 = 3
a 2 = 3 · ( - 2 ) = - 6
a 3 = 3 · 4 = 12
a 4 = 3 · ( - 8 ) = - 24
a 5 = 3 · 16 = 48
3 - 6 + 12 - 24 + 48 = 33
Answer: C ) 33