Math

QuestionFind the general term of the series: 3, 5, 7, ... which can be expressed as an=3+2(n1)a_n = 3 + 2(n-1).

Studdy Solution

STEP 1

Assumptions1. The series is an arithmetic sequence (a sequence of numbers in which the difference between any two consecutive terms is constant). . The first term of the series is3.
3. The common difference of the series is (the difference between any two consecutive terms).

STEP 2

We can express the nth term of an arithmetic sequence using the formulaan=a1+(n1)da_n = a1 + (n -1) \cdot dwhere- ana_n is the nth term- a1a1 is the first term- nn is the term number- dd is the common difference

STEP 3

Now, plug in the given values for the first term and the common difference into the formula.
an=3+(n1)2a_n =3 + (n -1) \cdot2

STEP 4

implify the equation.
an=3+2n2a_n =3 +2n -2

STEP 5

Combine like terms.
an=2n+1a_n =2n +1So, the nth term of the series \{3,5,7, \ldots\} is 2n+12n +1.

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