Question

Consider the arithmetic sequence presented in the table below. What is the first term, a1, and the 22nd term of the sequence?

n 5 71
an 42 636

Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference.

Answer 1

`a_(5)=42=\ \textgreater \ a_(5) = a_(1) +(5-1)d=42 a_(71) =636=\ \textgreater \ a_(71)=a_(1)+(71-1)d=636`


Subtract the frist equation from the second equation:

=> 70d - 4d = 636 - 42

66d = 514

=> d = 514 / 66 = 9

Now, find the first term,
`a_(1)`


`a_(1) =42-4d=42-4(9)=42-36=6`

And the 22nd term is:


`a_(22) = a_(1) +d(22-1)=6+9(21)=6+189=195`