Question

Within the set of whole numbers , one set of numbers satisfies the recursive formula an=(an-1)^2-an-1, when a4=870 what are the first two terms of the sequence?

Answer 1

A

Explanation:

Answer 2

Answer: 3 and 6 will be the first and second term of the given series respectively.

Explanation: since it is given-
`a_n=(a_(n-1) )^2-a_(n-1)` and
`a_4=870`

so, by replacing n by 4, we will get-
`a_4=a_3^2-a_3`⇒870=
`a_3^2-a_3`⇒
`a_3^2-a_3-870=0`

after solving this equation we will get,
`a_3= -29` and 30.

If
`a_3= -29`, but it is not a whole number.

Thus,
`a_3=30` will be the value of third term of the given series.

Again, by applying the given condition
`a_n=(a_(n-1) )^2-a_(n-1)`,
`a_2= 6` or -5 (not possible), so,
`a_2=6` will be the second term.

Similarly,
`a_1=3` or -2 but we will go to the whole number.

Thus,
`a_1=3` will be the first term.