Help me find a33

Question

If a3=63 and the a13=33

Answer 1

use the general formula for arithmetic sequences( I'm assuming it's arithmetic, there are all types of sequences!!)

a_n = a₁ + d(n-1)   plug into 2 separate equations

 

63 = a₁ + d(2)

33 = a₁ + d(12)

 

If you now subtract these 2 equations you get

30 = -10d

-3 = d now substitute this back in to get

63 = a₁+ (-3)(2)

69 =a₁

 

So your sequence has the formula a_n= 69-3(n-1)

You can check that this is correct by plugging in n=3 to get 63 and n=13 to get 33.

 

So now plug in n=33 to gin that a₃₃= -27

 

Hope this helped