Find the given term of each arithmetic sequence

Question

-2,-5,-8,-11,...; 41st term

Answer 1

For an arithmetic sequence, the n^th term, a_n, is given by the formula             a_n = a₁ + (n-1)d, where a₁ is the first term of the sequence and d is the common difference.  

 

So, for the sequence -2, -5, -8, -11,... , the sequence is arithmetic with common difference d = -3.

 

So, a_n = -2 + (n-1)(-3) = -3n + 1

 

Therefore, a₄₁ = -3(41) + 1 = -122