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19 votes
19 votes
Write an explicit formula that represents the sequence defined by the followingrecursive formula:a1 = 10 and an = an-1 + 9

User Hitesh Israni
by
2.6k points

1 Answer

14 votes
14 votes

According to the given problem,


\begin{gathered} a_n=a_(n-1)+9 \\ a_1=10 \end{gathered}

Solve for the successive terms by substituting n=2,3,4,5,....


\begin{gathered} a_2=a_1+9=10+9=19 \\ a_3=a_2+9=19+9=28 \\ a_4=a_3+9=28+9=37 \\ a_5=a_4+9=37+9=46 \end{gathered}

So the sequence is obtained as,


10,19,28,37,46,\ldots\ldots\ldots

Onserve that this is an Arithmetic Progression with first term (a) 10, and the common difference (d) 9 units.

So the nth term of the AP is given by,


\begin{gathered} a_n=a+(n-1)d \\ a_n=10+(n-1)9 \\ a_n=10+9n-9 \\ a_n=1+9n \end{gathered}

This the explicit formula representing the sequence is obtained as,


a_n=1+9n

User Dinsim
by
3.1k points
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