Question: Let {an} (n ³ 1) be a sequence such that a1 = 1, and 3an+1 – 3a<sub...

Question

Let {a_n} (n ³ 1) be a sequence such that a₁ = 1, and 3a_n+1 – 3a_n = 1 for all n ³ 1. Then a₂₀₀₂ is equal to-

Answer 1

a₁ = 1

3a_n+1 – 3a_n = 1

a_{n + 1} = = ,

a₂ = $\frac { 1 } { 3 }$

a₃ = a₂ + $\frac { 1 } { 3 }$ = = 1 + $\frac { 2 } { 3 }$

a₄ = a₃ + $\frac { 1 } { 3 }$ = $1 + \frac { 2 } { 3 } + \frac { 1 } { 3 }$ = 1 + $\frac { 3 } { 3 }$

.... .......... ................. .........

a₂₀₀₂ = 1 + $\frac { 2001 } { 3 }$ = 1 + 667 = 668

Question: Let {a<sub>n</sub>} (n ³ 1) be a sequence such that a<sub>1</sub> = 1, and 3a<sub>n+1</sub> – 3a<sub...