Note that in general an arithmetic sequence is

\[ (0) a, a+d, a+2d, a+3d, a+4d, \dots\]

and the $n$th term is given by

\[(1) a_n=a+(n-1)d. \]

With these in mind, we try to answer the questions.

16) The 11th term is 53, using formula (1) we have

\[a_{11}=a+(11-1)d=a+10d=53. (3)\]

The sum of 5th and 7th term is 56. This means

\[a_5+a_7=(a+4d)+(a+6d)=2a+10d=56. (4)\]

Paying attention to (3) and (4), we see that we have two equations and two unknowns that we need to solve. Substract (3) from (4) to get

\[(4)-(3) \Rightarrow (2a+10d)-(a+10d)=56-53 \Rightarrow a=3.\]

Substituting $a=3$ in (3) we get

\[3+10d=53 \Rightarrow 10d=50 \Rightarrow d=\frac{50}{10}=5 \Rightarrow d=5.\]

Utilizing (0) we write the first three terms of the sequence

\[3, 3+5, 3+2 (5), \dots\]

So the first three terms are

\[3, 8, 13.\]

17) The sum of the first two terms is 15:

\[a+(a+d)=15 \Rightarrow 2a+d=15. (5)\]

The sum of the next two terms (3rd and 4th) is 43:

\[(a+2d)+(a+3d)=43 \Rightarrow 2a+5d=43. (6)\]

Subtracting equation (5) from equation (6) we get

\[(6)-(5) \Rightarrow (2a+5d)-(2a+d)=43-15 \Rightarrow 4d=28 \Rightarrow d=7.\]

Substituting $d=7$ in equation (5) we get

\[2a+7=15 \Rightarrow 2a=8 \Rightarrow a=4.\]

So the first three terms of the sequence are

\[a, a+d, a+2d, \dots\]

that is

\[4,4+7,4+2(7), \dots\]

So the first three terms are

\[4, 11, 18.\]