Computations for exercise 1

fib[0] = 0
fib[1] = 1
fib[n_] := fib[n-1] + fib[n-2]/; n ≥ 2

Table[fib[n], {n, 1, 20}]

oddSum[n_] := (∑_(k=1)^n)fib[2k-1]

Table[oddSum[n], {n, 1, 10}]

evenSum[n_] := (∑_(k=1)^n)fib[2k]
Table[evenSum[n], {n, 1, 10}]

altSum[n_] := (∑_(k=0)^n)(-1)^k fib[k]
Table[altSum[n] , {n, 1, 10}]

squareSum[n_] := (∑_(k=0)^n)fib[k]^2
Table[squareSum[n] , {n, 1, 10}]

When is fib[n]  divisible by 7?

Table[Mod[fib[n], 7], {n, 1, 30}]