Question

Vera and Fenyang were asked to find an explicit formula for the sequence 26,10,-6,-22,...

Answer 1

`a_(n)` = 42 - 16n

Explanation:

Note there is a common difference d between consecutive terms

d = 10 - 26 = - 6 - 10 = - 22 - ( - 6)) = - 16

This indicates that the sequence is arithmetic with n th term ( explicit formula )

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 26 and d = - 16, thus

`a_(n)` = 26 - 16(n - 1) = 26 - 16n + 16 = 42 - 16n

Answer 2

Good evening ,

Answer:

Un = -16n +42

Explanation:

Un = U1 + (n-1)r

U1 = 26

r = 10-26 = -16

Un = U1 + (n-1)r

= 26 + (n-1)(-16)

= 26 - 16n + 16

= -16n +42.

:)