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

We are given sequence is 2 , 4 , 8 ,16 , 32 , .....Firstly , we will check whether it is geometric sequenceChecking geometric sequence:We will find common ratio between successive terms and then we check whether they are equalr1=(second term)/(first term)[tex] r_1=\frac{4}{2}=2 [/tex]r2=(third term)/(second term)[tex] r_2=\frac{8}{4}=2 [/tex]r3=(fourth term)/(third term)[tex] r_3=\frac{16}{8}=2 [/tex]r4=(fifth term)/(fourth term)[tex] r_4=\frac{32}{16}=2 [/tex]we can see that all four ratios are same[tex] r_1=r_2=r_3=r_4=2 [/tex]so, this is geometric sequence Calculation of general term:We got common ratio is [tex] r=2 [/tex]Let's assume number of terms is nfirst term is 2[tex] a_1=2 [/tex]now, we can use formula [tex] a_n=a_1 (r)^{n-1} [/tex]we can plug valuesand we get [tex] a_n=2(2)^{n-1} [/tex][tex] a_n=2^1(2)^{n-1} [/tex][tex] a_n=(2)^{n-1+1} [/tex][tex] a_n=(2)^{n} [/tex]..................Answer