9514 1404 393
Answer:
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
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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, ...
