What is a40 for the arithmetic sequence presented in the table below?
Hint: An = A1 + d(n - 1), where a1 is the first term and d is the common difference.

Question

What is a40 for the arithmetic sequence presented in the table below? 
Hint: An = A1 + d(n - 1), where a1 is the first term and d is the common difference.

anonymous · Answer

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campbell_st · Answer

ok... so you know $$A_{8} = 60 ~~~and~~~~A_{12} = 48$$

so the sequence is decreasing... so the common difference is negative. 

so just do some simple arithmetic, remembering that the common difference is always the same value. 

$$\frac{(48 - 60)}{(12 - 8)} = $$

and from there you can find the 1st term

anonymous · Answer

So -3 is the first term?

anonymous · Answer

@campbell_st

campbell_st · Answer

no -3 is the common difference... to to find the 1st term, use this for d, and n = 8 with 60

so 

$$60 = a_{1} + (8 -1) \times (-3)$$

now solve for your 1st term

anonymous · Answer

I got 81 for the the 1st term. Is that correct? @campbell_st

campbell_st · Answer

that's correct so now you can find the 40th term using the formula 

$$a_{40} = a_{1} + (40-1) \times (-3)$$

hope it helps

anonymous · Answer

it did thanks!