MATH SOLVE

4 months ago

Q:
# Find the explicit formula for the general nth term of the arithmetic sequence described below. Simplify your answer.a1= -3 and a10= 69

Accepted Solution

A:

[tex]\boxed{a_{n}=-3+8(n-1)}[/tex]Explanation:The explicit formula for the general nth term of the arithmetic sequence is given by:[tex]a_{n}=a_{1}+d(n-1) \\ \\ \\ Where: \\ \\ a_{n}:nth \ term \\ \\ n:Number \ of \ terms \\ \\ a_{1}:First \ term \\ \\ d:common \ difference[/tex]Here we know that:[tex]a_{1}=-3 \\ \\ a_{10}=69[/tex]So, our goal is to find the common difference substituting into the formula:[tex]a_{10}=a_{1}+d(10-1) \\ \\ 69=-3+d(9) \\ \\ Solving \ for \ d: \\ \\ 9d=69+3 \\ \\ 9d=72 \\ \\ d=8[/tex]Finally, we can write the explicit formula as:[tex]\boxed{a_{n}=-3+8(n-1)}[/tex]Learn more:Geometric series: