confused wrote:5, 13, 25, 41, 61
5, 5+8, 5+8+12, 5+8+12+16, 5+8+12+16+20
then what?
Now you need to find a way of relating the above pattern to the "n" which stands for the "n-th" place.
The first entry is just 5.
The second entry is 5 + 2(4).
The third entry is 5 + 2(4) + 3(4) = 5 + 5(4).
The fourth entry is 5 + 2(4) + 3(4) + 4(4) = 5 + 9(4).
The fifth entry is 5 + 2(4) + 3(4) + 4(4) + 5(4) = 5 + 14(4).
The multipliers of 4, at each stage, are 2, 5, 9, and 14. Note that these grow by amounts that increase, at each stage, by 1. Can we use this at all, in relating the pattern to "n"?
The first multiplier, when n = 1, is 0.
The second multiplier, when n = 2, is 2.
The third multiplier, when n = 3, is 5.
The fourth multipler, when n = 4, is 9.
The fifth multipler, when n = 5, is 14.
From what you've learned about
the method of common differences, you know how to determine that the pattern for these multipliers in terms of "n".
Then plug this pattern into the larger pattern: 5 + (pattern for the n-th term's multipler)(4).
Gotta run! I'll try to respond more later, if you like.