JEE Main 2022 · 24 Jun · Shift 2 · Mathematics Q25

MathematicsInteger+4 / -1Question 25 of 90

The remainder on dividing $1+3+3^2+3^3+\dots+3^{2021}$ by 50 is ______.

Your answer

Answer and worked solution

Official answer: 4

Sum. $1+3+\dots+3^{2021}=\dfrac{3^{2022}-1}2$ .

Mod 100. $3^{20}\equiv1\pmod{100}$ and $2022=20\cdot101+2$ , so $3^{2022}\equiv9$ and $3^{2022}-1\equiv8\pmod{100}$ .

Halve. $\dfrac{3^{2022}-1}2\equiv4\pmod{50}$ .

Answer: 4

JEE Main 2022 · 24 Jun · Shift 2, Mathematics question 25