Question

Fill in the blanks to write the rule for the sequence below: 32,42,52,62…. an=______n+_______

Answer 1

the rule for sequence below 32,42,42...

is

an = 10n + 22

Answer 2

`a_(n)` = 10n + 22

Explanation:

there is a common difference between consecutive terms, that is

42 - 32 = 52 - 42 = 62 - 52 = 10

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 32 and d = 10 , then

`a_(n)` = 32 + 10(n - 1) = 32 + 10n - 10 = 10n + 22