If a1 = 5 and a n =
4an-1 then find the value of a6

9514 1404 393

  5120

Step-by-step explanation:

The recursive formula ...

  a[1] = 5

  a[n] = 4·a[n-1]

defines a sequence with first term 5 and common ratio 4. The explicit formula for a term in this sequence can be written ...

  a[n] = 5·4^(n-1)

We can use this formula to find a[6]:

  a[6] = 5·4^(6-1) = 5·1024

  a[6] = 5120

If you like, you can write out the first 6 terms of the sequence using the recursive formula. Each is 4 times the previous.

  5, 20, 80, 320, 1280,  5120, ...

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.