Write a rule for the nth term and find the 45th term for the arithmetic sequence with a10=1 and d = -6.

Question

I have trouble with arithmetic sequences, could someone help me out?

This is all I have so far, which isn't much at all:
an = a1 + (n-1) d
an = a1 + (n-1)-6

Answer 1

here is the correct way to write the formula for the nth term, when the constant difference d is negative 6:

a_n = a₁ + (n-1)(-6)

 

When n=10, a₁₀ = 1.  The prior term would be six more, because successive terms are 6 lower.

 

1 = a₁ + (10-1)(-6) when n = 10; this allows you to solve for a₁, which will be 55. 

 

Therefore a_n = 55 + (n-1)(-6)