Question

Find the next four terms of the following sequence: a_1=3a_n=2a_n-1+n

Answer 1

Given:

`\begin{gathered} \text{ A}_1\text{ = 3} \\ \text{ A}_n=2A_(n-1)\text{ + n} \end{gathered}`

Where,

n = term position

Since we already got the 1st term (A1 = 3), let's determine the next four terms.

2nd term: n = 2

`\text{ A}_2=2A_(2-1)\text{ + }2`
`\text{ A}_2=2A_1\text{ + }2`
`\text{ A}_2=2(3)\text{ + }2`
`\text{ A}_2=6\text{ + }2`
`\text{ A}_2=8`

3rd term: n = 3

`\text{ A}_3=2A_(3-1)\text{ + }3`
`\text{ A}_3=2A_2\text{ + }3`
`\text{ A}_3=2(8)_{}\text{ + }3`
`\text{ A}_3=16_{}\text{ + }3`
`\text{ A}_3=19`

4th term: n = 4

`\text{ A}_4=2A_(4-1)\text{ + }4`
`\text{ A}_4=2A_3\text{ + }4`
`\text{ A}_4=2(19)\text{ + }4`
`\text{ A}_4=38\text{ + }4`
`\text{ A}_4=42`

5th term: n = 5

`\text{ A}_5=2A_(5-1)\text{ + }5`
`\text{ A}_5=2A_4\text{ + }5`
`\text{ A}_5=2(42)\text{ + }5`
`\text{ A}_5=84\text{ + }5`
`\text{ A}_5=89`

Therefore, the next four terms of the following sequence are: 8, 19, 42, 89.