Question
Given the terms of an arithmetic sequence, a_1=−19 and a_{26}=56 find a formula for the general term.
Given the terms of an arithmetic sequence, a_1=−19 and a_{26}=56 find a formula for the general term.
Let d the common difference of the arithmetic sequence.
Use the formula for general terms,
a_n=a_1+(n-1)d
d=\dfrac{a_n-a_1}{n-1}
=\dfrac{a_{26}-a_1}{26-1}
=\dfrac{56-(-19)}{25}
=\dfrac{75}{25}
=3
Next, use the first term a_1=−19 and the common difference d=3 to find a formula for the general term.
a_n=-19+(n-1)3 =3n-22