Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d=−6.

Question

I have tried everything I can possibly think of. I have taken this quiz four times now. I am desperate.

Here's what I have come up with previously if it is any help, or if you can tell me where I have gone wrong.

a1+(n-1)(d)=an

a1+(10-1)(-6)=-1=an=a10

a1+(-60+6)=-1

a1+(-60+6)+60-6=-1+60-6

a1=53

then,

53+(45-1)(-6)=a45

53+(-270+6)=a45

53-270+6=-211=a45

therefore -211=a45

However, this was incorrect. Is there another way to solve this equation, or do you see an error in my work? If so, I am begging you, please, please, please, help me figure this out. Thank you!

Answer 1

First use standard notation

a₁₀ = a₁ + (n - 1)(d)

a₁₀ = a₁ + (9)(-6)

1 = a₁ - 54

55 = a₁

a₄₅ = 55 + (44)(-6)