Question

6. If the information given represents an arithmetic

sequence, find the 27th term.

a_1 = 49 and a_8 = 14

Answer 1

Since consecutive terms differ by a constant k in this sequence, we have

`a_8 = a_7 + k`

`a_8 = (a_6+k)+k = a_6+2k`

`a_8 = (a_5+k)+2k=a_5+3k`

and so on down to

`a_8 = a_1 + 7k`

Solve for k :

14 = 49 + 7k ⇒ -35 = 7k ⇒ k = -5

We then do the same as above but in the reverse direction:

`a_9 = a_8+k`

`a_(10) = a_9+k = a_8+2k`

`a_(11) = a_(10)+k = a_8+3k`

and so on, up to

`a_(27) = a_8 + 19k = \boxed{-81}`