The value of [tex]\rm a_{1}, \rm a_{2}, \rm a_{3}, \rm a_{4}[/tex] for a given expression [tex]\rm a_{n+1} = {\frac {a_{n}} {n+2}[/tex] is 1, 1/3, 1/12, and 1/60.
We have given [tex]\rm a_{1} =1[/tex] and [tex]\rm a_{n+1} = {\frac {a_{n}} {n+2}[/tex] for n≥1 we need to determine the value of [tex]\rm a_{1}, \rm a_{2}, \rm a_{3}, \rm a_{4}[/tex] .
How do you solve for n terms?
To solve for n terms, we will substitute the value of n = 1,2,3,4 and so on sequence-wise in the given expression.
if n = 1
[tex]\rm a_{1+1} = {\frac {a_{1}} {1+2}[/tex]
[tex]\rm a_{2} = {\frac {a_{1}} {3}}\\\rm a_{2} = {\frac{1} {3}[/tex]
if n = 2
[tex]\rm a_{2+1} = {\frac {a_{2}} {2+2}}\\\rm a_{3} = {\frac {1/3} {4}}\\\rm a_{3} = 1/12[/tex]
if n = 3
[tex]\rm a_{3+1} = {\frac {a_{3}} {3+2}}\\\rm a_{4} = {\frac {a_{3}} {5}}\\\rm a_{4} = 1/12 \times 1/5\\\rm a_{4} = 1/60[/tex]
So, the value of [tex]\rm a_{1}, \rm a_{2}, \rm a_{3}, \rm a_{4}[/tex] is 1, 1/3, 1/12, and 1/60.
Learn more about the substitution of values here:
https://brainly.com/question/20052796
