For any term in an arithmetic progression:
nth term =a+(n−1)d
Where a is the first term, d is the common difference, and n is the position of the term.
Given that the 5th term is 7:
a+(5−1)d=7
a+4d=7 -----(Equation 1)
Given that the 9th term is 13:
a+(9−1)d=13
a+8d=13 -----(Equation 2)
Subtracting Equation 1 from Equation 2:
(a+8d)−(a+4d)=13−7
a+8d−a−4d=6
4d=6
d=46
d=1.5
Substituting d=1.5 into Equation 1:
a+4(1.5)=7
a+6=7
a=1
The 15th term is:
a+(15−1)d
=1+14(1.5)
=1+21
=22
Therefore, the 15th term is 22.