Question

For the following exercises, find the specified term given two terms from an arithmetic sequence. 

a1 = 33 and a7 = −15. Find a4 .

Answer 1

Consider an arithmetic sequence with a1 = 33 and a7 = -15

Use the formula for nth term of an arithmetic sequence,

an = a1 + (n – 1)d ...... (1)

 

Substitute a1 = 33, n = 7 and a7 = -15 in formula (1),

-15 = 33 + (7 – 1)d

-15 = 33 + 6d

 6d = -15-33

 6d = 48

 

Division by 6 gives,

d = -48/6

d = -8

 

Compute forth term a4 of given sequence, substitute a1 = 33 and d = -8 in equation (1),

a4 = 33 + (4 – 1) × (-8)

     = 33 + 3 × (-8)

     = 33 – 24

     = 9

 

Therefore, fourth term of given arithmetic sequence is a4 = 9.

Therefore, fourth term of given arithmetic sequence is a4 = 9.