Math

QuestionFind the explicit formula for the sequence with a1=1a_{1}=-1 and common difference d=10d=-10.

Studdy Solution

STEP 1

Assumptions1. We are dealing with an arithmetic sequence. . The first term of the sequence, denoted as a1a_{1}, is -1.
3. The common difference of the sequence, denoted as dd, is -10.

STEP 2

The explicit formula for an arithmetic sequence is given byan=a1+(n1)da_{n} = a_{1} + (n-1) \cdot dwhere ana_{n} is the nth term, a1a_{1} is the first term, dd is the common difference, and nn is the term number.

STEP 3

Now, plug in the given values for the first term and the common difference into the formula.
an=1+(n1)10a_{n} = -1 + (n-1) \cdot -10

STEP 4

implify the formula.
an=110n+10a_{n} = -1 -10n +10

STEP 5

Further simplify the formula.
an=910na_{n} =9 -10nSo, the explicit formula for the arithmetic sequence is an=910na_{n} =9 -10n.

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