Question

Which one of the following number will completely divide $(3^{25}+3^{26}+3^{27}+3^{28})$?

• A. $11$
• B. $16$
• C. $25$
• D. $30$

Answer 1

Answer: (D)

$30$

$3^{25}+3^{26}+3^{27}+3^{28}$
$=3^{25}(1+3+3^2+3^3)$
$=3^{25}\times (1+3+9+27)=3^{25}\times 40$
$=3^{24}\times 3\times 4\times 10=3^{24}\times 4\times 30$ which is divisible by $30$