Question

Find the first term and rule for the nth term of the arithmetic sequence if A11=43 and d =5

Answer 1

We have an arithmetic sequence with:

• a_11 = 43,

,

• d = 5.

The general formula for an arithmetic sequence is:

$a_n=a_1+(n-1)\cdot d._{}$

For n = 11, we have:

$\begin{gathered} a_{11}=a_1+(11-1)d, \\ a_{11}=a_1+10d\text{.} \end{gathered}$

Replacing the data of the problem we the equation above, we have:

$\begin{gathered} 43=a_1+10\cdot5, \\ 43=a_1+50, \\ a_1=43-50, \\ a_1=-7. \end{gathered}$

Answer

The first term of the series is -7.