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kolbaska11 [484]
3 years ago
11

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

Mathematics
1 answer:
Nuetrik [128]3 years ago
5 0

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=\frac{4}{2}=2

r2=(third term)/(second term)

r_2=\frac{8}{4}=2

r3=(fourth term)/(third term)

r_3=\frac{16}{8}=2

r4=(fifth term)/(fourth term)

r_4=\frac{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


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