Question

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

Answer 1

Answer: $\sum_{n=1}^{5}4^n=1364$

Step-by-step 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

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

So, our equation becomes ,

$a=4 \\\\r=\frac{a_2}{a_1}=\frac{4^2}{4}=4\\\\S_5=\frac{4(4^5-1)}{4-1}\\\\S_5=1364$

Hence ,

$\sum_{n=1}^{5}4^n=1364$

Answer 2

Answer: 1364

Step-by-step 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 = $\frac{4(1 - 4^{5})}{1 - 4}$

  = $\frac{4(1 - 1024)}{-3}$

  = $\frac{4(-1023)}{-3}$

  = $\frac{-4092}{-3}$

  = 1364