SOLUTION: what is the 22nd term in the arithmetic sequences in which a[4] is 73 and a[10] is -11

Algebra ->  Sequences-and-series -> SOLUTION: what is the 22nd term in the arithmetic sequences in which a[4] is 73 and a[10] is -11      Log On


   

Question 818091: what is the 22nd term in the arithmetic sequences in which a[4] is 73 and a[10] is -11
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
what is the 22nd term in the arithmetic sequences in which a[4] is 73 and a[10] is -11
an = a1 + (n-1)d

a4 = a1 + (4-1)d = 73
a10 = a1 + (10-1)d = -11

a4 = a1 + 3d = 73
a10 = a1 + 9d = -13

a1 + 3d = 73
a1 + 9d = -11

Solve the first one for a1

a1 = 73 - 3d

Substitute 73 - 3d for a1 in the second
equation:

73 - 3d + 9d = -11
     73 + 6d = -11
          6d = -84
           d = -14

Substitute -14 for d in

a1 = 73 - 3d 

a1 = 73 - 3(-14)

a1 = 73 - 3(-14) = 73 + 42 = 115

To find the 22nd term we substitute 

a1 = -53

n = 22

d = -14 into:

an = a1 + (22-1)(-14)

a22 = 115 + (21)(-14)

a22 = 115 + (21)(-14) = 115 - 294 = -179

Checking:

115,101,87,73,59,45,31,17,3,-11,-25,-39,-53,
-67,-81,-95,-109,-123,-137,-151,-165,-179

Edwin