Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74.
-20.5
-151
-22.75
-144

Question

Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74. 
   -20.5 
 -151 
 -22.75 
 -144

campbell_st · Answer

ok to find a term in an arithmetic sequence use 

$$a_{n} = a + (n - 1) \times d$$

the information in your question can be used to find the common difference , d

$$-74 = 38 + (17 -1) \times d.......or..... -74 = 38 + 16d$$

solve for d. 

then substitute n = 27, a = 38 and the value of d into the formula above to find the 27th term

anonymous · Answer

I got 227 but none of those are the answers?

campbell_st · Answer

well I think you should know the common difference is negative 

-112 = 16d

d = -7

so the 27th term 

$$a_{27} = 38 + (27 -1) \times (-7)$$

anonymous · Answer

Thank you!