Question

3^51+3^52+3^53+3^54+3^55 is divisible by​

Answer 1

Answer:

Step-by-step explanation:

3^51+3^52+3^53+3^54+3^55 = (3^51)*(1+3+9+27+81)

= (3^51)*(121)

= (3^51)*(11^2)

So the formula will be divisible by (3^m)*(11^n)

When m and n is an integer where m is not lesser than 0, m is not greater than 51, n is not lesser than 0 and n is not greater than 2

Answer 2

$3^{51} +3^{52} +3^{53} +3^{54} +3^{55}$ is divisible by 11 and 121.

Step-by-step explanation:

We have,

$3^{51} +3^{52} +3^{53} +3^{54} +3^{55}$

=$3^{51} (1+3^{1} +3^{2} +3^{3} +3^{4})$

$=3^{51} (1+3+9 +27 +81)$

$=3^{51} (121)$

∵ $=3^{51} (121)$ is divisible by 11 and 121.

Hence, $3^{51} +3^{52} +3^{53} +3^{54} +3^{55}$ is divisible by 11 and 121.