Write an explicit formula for the sequence given in the recursive formula below:
a1=−22
an+1=an+7
(1 point)
Responses
an=7−22n
A sub n is equal to 7 minus 22 n
an=−22+7(n−1)
A sub n is equal to negative 22 plus 7 times open paren n minus 1 close paren
an=7−22(n−1)
A sub n is equal to 7 minus 22 times open paren n minus 1 close paren
an=−22+7n
Substitute the value of a_{n+1} from the recursive formula into the equation a_{n+1} = a_n + 7:
a_n = a_{n+1} - 7
a_n = a_n + 7 - 7
a_n = a_n
Therefore, the explicit formula for the sequence is simply:
a_n = -22.
Huh???
I assume you mean an arithmetic sequence with first term = -22 and change =7
A(n+1) = A(n) + 7
An=−22+7(n−1)
I apologize for the confusion. Yes, you are correct. For an arithmetic sequence with a first term of -22 and a common difference of 7, the formula should be:
A_n = -22 + 7(n-1)