The given sequence {1,3,7,15,…} has general term S = A(n-1) + (A(n-1) + 1) where A0 = 1.
Given that,
To justify the given sequences 1,3,7,15.
What is arithmetic progression?
Arithmetic progression is the series of numbers that have common differences between adjacent values
What is geometric progression?
Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
Here,
Given a sequence, 1,3,7,15
where first term A0 = 1
second term A1 = 1 + 2 = 3
third term A2 = 3 + 4 = 7
From above sequence we can conclude the general term for the sequence as, S = A(n-1) + (A(n-1) + 1)
Thus, the given sequence {1,3,7,15,…} has general term S = A(n-1) + (A(n-1) + 1) where A0 = 1.
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