Question

If a1=10 and an=an-1 +1 whats the value of a4

Answer 1

Given:

`a_1=10\text{ and }a_n=a_(n-1)+1.`
`\text{ Substitutting n=2 in }a_n=a_(n-1)+1,\text{ we get}`

`a_2=a_(2-1)+1`

`a_2=a_1+1`
`\text{Substitute }a_1=10,\text{ we get }`

`a_2=10+1`
`\text{ We get }a_2=11.`

`\text{ Substitutting n=3 in }a_n=a_(n-1)+1,\text{ we get}`

`a_3=a_(3-1)+1`

`a_3=a_2+1`

`\text{Substitute }a_2=11,\text{ we get }`

`a_3=11_{}+1`

`\text{ We get }a_3=12.`

`\text{ Substitutting n=4 in }a_n=a_(n-1)+1,\text{ we get}`

`a_4=a_(4-1)+1`

`a_4=a_3+1`

`\text{Substitute }a_3=12,\text{ we get }`

`a_4=12+1`

`a_4=13`
`\text{ Hence the required value is }a_4=13.`

The answer is

`a_4=13`