Identify the 42nd term of an arithmetic sequence where a1 = -12 and a27 = 66.

Question

callisto · Answer

$$a_n = a_1 + (n-1)d$$where n is the nth term, and d is the common difference.
First find the common difference.
$$a_{27} = a_1 + (27-1)d$$$$66= -12 + (26)d$$Solve d.
Then, sub. n=42, $a_1=-12$  and the value of d you've found into the formula to find the 42nd term.
$$a_{42} = -12 + (42-1)d = ...$$

anonymous · Answer

Thanks! so, if d=3, a_42= 111? Thanks so much!!
do you think you could help me answer another similar question?

callisto · Answer

Yup. :)

anonymous · Answer

Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74.

uh and also

Identify the 31st term of an arithmetic sequence where a 1 = 26 and a22 = -226.

:) thanks again!

callisto · Answer

Please post a new question in a new post next time. Thanks!
Btw, can you try to do it first? Use the above formula, plug in the suitable values and solve it.

anonymous · Answer

oh ok!!! sorry i am new lol, still getting used to the layout/rules

callisto · Answer

Welcome to OpenStudy! You're recommended to read the Code of Conduct at http://www.openstudy.com/code-of-conduct when you have time. Btw, what have you got for finding the 27th term question?

anonymous · Answer

-74=38+(17-1)d
-112=16d
d=-7
and then....

callisto · Answer

a27 = a1 + (n-1)d = ...?

anonymous · Answer

so a_27= -144?

callisto · Answer

Yup :)
You can try the next one now, can you?

anonymous · Answer

yeah, i think i got it! thank you so much for all your help, i was not getting this concept at all!

callisto · Answer

Welcome :)