Question

For the following exercises, write the first five terms of the arithmetic series given two terms.

a13 = −60, a33 = −160

Answer 1

Consider an arithmetic sequence with a13 = -60 and a33 = -160

Use the formula for nth term of an arithmetic sequence,

an = a1 + (n – 1)d ...... (1)

 

Substitute n = 13 and a13 = -60 in formula (1),

-60 = a1 + (13 – 1)d

-60 = a1 + 12d ...... (2)

 

Substitute n = 33 and a33 = -160 in formula (1),

-160 = a1 + (33 – 1)d

-160 = a1 + 32d ...... (3)

 

Subtract equation (2) -60 = a1 + 12d from (3) -160 = a1 + 32d,

-160 = a1 + 32d

  -60 = a1 + 12d

-100 = 20d

 

Division by 20 gives,

d = -100/20

d = -5

 

Substitute d = -5 in equation (2) -60 = a1 + 12d,

-60 = a1 + 12 × (-5)

 a1 = -60 + 60

 a1 = 0

 

Compute second term of the sequence as follows:

a2 = a1 + d

     = 0 + (-5)

     = -5

 

Compute third term of the sequence as follows,

a3 = a2 + d

     = -5 +(-5)

     = -10

 

Compute forth term of the sequence as follows:

a4 = a3 + d

     = -10 + (-5)

     = -15

 

Compute fifth term of the sequence as follows:

a5 = a4 + d

     = -15 + (-5)

     = -20

Therefore, first five terms of given arithmetic sequence are {0, -5, -10, -15, -20}.

Therefore, first five terms of given arithmetic sequence are {0, -5, -10, -15, -20}.