Question

The general term for the sequence 2, 4, 8, 16, 32, . . . is

Answer 1

a1: 2 r1: 2

Explanation

just did it on edge :)

the answer for the second part is the 1st and 4th formulas

Answer 2

We are given

sequence is 2 , 4 , 8 ,16 , 32 , .....

Firstly , we will check whether it is geometric sequence

Checking geometric sequence:

We will find common ratio between successive terms

and then we check whether they are equal

r1=(second term)/(first term)

`r_1=(4)/(2)=2`

r2=(third term)/(second term)

`r_2=(8)/(4)=2`

r3=(fourth term)/(third term)

`r_3=(16)/(8)=2`

r4=(fifth term)/(fourth term)

`r_4=(32)/(16)=2`

we can see that all four ratios are same

`r_1=r_2=r_3=r_4=2`

so, this is geometric sequence

Calculation of general term:

We got

common ratio is

`r=2`

Let's assume

number of terms is n

first term is 2

`a_1=2`

now, we can use formula

`a_n=a_1 (r)^(n-1)`

we can plug values

and we get

`a_n=2(2)^(n-1)`

`a_n=2^1(2)^(n-1)`

`a_n=(2)^(n-1+1)`

`a_n=(2)^(n)`..................Answer