Question

Find the first term and the common difference of the arithmetic sequence whose 11th term is 26 and 13th term is 32 .First term is Common difference is

Answer 1

We have a sequence which have the 11th term equal to a11 = 26 and the 13th term is a13 = 32.

If the difference is d, then, we can write:

`\begin{gathered} a_(12)=a_(11)+d \\ a_(13)=a_(12)+d \\ \Rightarrow a_(13)=a_(11)+d+d=a_(11)+2d \\ a_(13)-a_(11)=2d \\ d=(a_(13)-a_(11))/(2) \\ d=(32-26)/(2) \\ d=(6)/(2) \\ d=3 \end{gathered}`

The common difference has to be d = 3.

We can use this to find the first term as:

`\begin{gathered} a_2=a_1+d \\ a_3=a_2+d=a_1+2d \\ \Rightarrow a_(11)=a_1+(11-1)d=a_1+10d \\ a_1=a_(11)-10d \\ a_1=26-10*3 \\ a_1=26-30 \\ a_1=-4 \end{gathered}`

Answer:

First term is -4.

Common difference is 3.