Question

PLEASE I NEED TO TURN THIS IN TOMORROW I NEED HELP PLEASE HELP ME

Answer 1

Answer: 1364

Explanation:

∑ 4ⁿ from n = 1 to 5

n = 1: 4¹ = 4

n = 2: 4² = 16

n = 3: 4³ = 64

n = 4: 4⁴ = 256

n = 5: 4⁵ = 1024

1364

You can also use the formula: S = [a(1 - rⁿ)]/(1 - r)

S =
`(4(1 - 4^(5)))/(1 - 4)`

=
`(4(1 - 1024))/(-3)`

=
`(4(-1023))/(-3)`

=
`(-4092)/(-3)`

= 1364

Answer 2

Answer:
`\sum_(n=1)^(5)4^n=1364`

Explanation:

Since we have given that

`\sum_(n=1)^(5)4^n`

Now, we know the rule for summation , we'll apply this ,

`\sum_(n=1)^(5)4^n\\=4^1+4^2+4^3+4^4+4^5\\`

Now, it becomes geometric progression, so we us the formula for sum of terms in g.p. which is given by

`S_n=(a(r^n-1))/(r-1)\\\\\text{where 'a' is the first term and 'r' is the common ratio}`

So, our equation becomes ,

`a=4 \\\\r=(a_2)/(a_1)=(4^2)/(4)=4\\\\S_5=(4(4^5-1))/(4-1)\\\\S_5=1364`

Hence ,

`\sum_(n=1)^(5)4^n=1364`