Question 1009259
Sequences of numbers that follow a pattern of adding a fixed number from one term to the next are called arithmetic sequences.

15. 
{{{-2}}},{{{5}}},{{{12}}},{{{19}}}...

For this sequence, if we add {{{7}}} to the first number we will get the second number,if we add {{{7}}} to the second number we will get the third number, and so on.
It means, the common difference (the difference between any two consecutive terms}}} is {{{d=7}}}
The d-value can be calculated by subtracting any two consecutive terms in an arithmetic sequence.

{{{d = a[n] - a[n - 1]}}}

if  {{{a[n]=19}}} and {{{a[n - 1]=12}}}, then

{{{d = 19 - 12}}} 

{{{d = 7}}} 

and your sequence will be

{{{-2}}},{{{5}}},{{{12}}},{{{19}}},{{{26}}},{{{33}}},{{{40}}},{{{47}}},{{{54}}},{{{61}}}...
. 
the nth term of the arithmetic sequence will be

{{{a[n] = a[1] + (n - 1)d }}}.......where {{{n}}} is any positive integer greater than {{{1}}}

then 10th term will be:

{{{a[10] = -2 + (10 - 1)7 }}}

{{{a[10] = -2 + 9*7 }}}

{{{a[10] = -2 + 63}}}

{{{a[10] = 61}}}


16. 
{{{13}}},{{{9}}},{{{5}}},{{{1}}}...

{{{d = a[n] - a[n - 1]}}}

if  {{{a[2]=9}}} and {{{a[1]=13}}}, then

{{{d = 9 - 13}}} 

{{{d = -4}}}


the nth term of the arithmetic sequence will be

{{{a[n] = a[1] + (n - 1)(-4) }}}

{{{a[n] = a[1] -4 (n - 1) }}}

then 10th term will be:

{{{a[10] = 13-4 (10 - 1) }}}

{{{a[10] = 13-4 (9) }}}

{{{a[10] = 13-36}}}

{{{a[10] = -23}}}