if the fifth term of an arithmetic sequence is -5 and the ninth term is -17, the first term of the sequence must be
a. -7
b. -5
c. -11
d. 7

Question

if the fifth term of an arithmetic sequence is -5 and the ninth term is -17, the first term of the sequence must be
a. -7
b. -5
c. -11
d. 7

campbell_st · Answer

well I suppose you need to set up the equations 

5th term

$$-5 = a_{1} + (5 -1)d~~~~or~~~-5 = a_{1} + 4d$$

9th term 

$$-17 = a_{1} + (9 -1)d~~~~~or~~~~~-17 = a_{1} + 8d$$

so the 2 equations are 

  -5 = a + 4d
-17 = a + 8d

subtract the equations to find d

then substitute the value into either equation to find a