# How do you write the first five terms of the sequence defined recursively a_1=3, a_(k+1)=2(a_k-1)?

Oct 16, 2017

3, 4, 6, 10, 18

#### Explanation:

When a sequence is defined recursively, the previous term is used to find the next term. Start by using ${a}_{1}$ to find ${a}_{2}$ (second term).

Substitute ${a}_{1}$ for ${a}_{k}$.
${a}_{1 + 1} = 2 \left({a}_{1} - 1\right)$
${a}_{2} = 2 \left({a}_{1} - 1\right)$
Because ${a}_{1} = 3$, substitute ${a}_{1}$ for $3$ to find ${a}_{2}$.
${a}_{2} = 2 \left(3 - 1\right)$
${a}_{2} = 2 \left(2\right)$
${a}_{2} = 4$ This is your second term!

Now use ${a}_{2}$ to find ${a}_{3}$ just like how you used ${a}_{1}$ to find ${a}_{2}$.
${a}_{2 + 1} = 2 \left({a}_{2} - 1\right)$
${a}_{3} = 2 \left(4 - 1\right)$
${a}_{3} = 2 \left(3\right)$
${a}_{3} = 6$ This is your third term!

Repeat these steps to find ${a}_{4}$ using ${a}_{3}$.
${a}_{3 + 1} = 2 \left({a}_{3} - 1\right)$
${a}_{4} = 2 \left(6 - 1\right)$
${a}_{4} = 2 \left(5\right)$
${a}_{4} = 10$ This is your fourth term!

Find ${a}_{5}$ using ${a}_{4}$.
${a}_{4 + 1} = 2 \left({a}_{4} - 1\right)$
${a}_{5} = 2 \left(10 - 1\right)$
${a}_{5} = 2 \left(9\right)$
${a}_{5} = 18$ This is your fifth term!

List the terms from least to greatest and separate the terms with commas.

Answer: 3, 4, 6, 10, 18