The 14th term of an a.p is 96,while the 25th term is 173. find the first term

Answer 1

In an Arithmetic Progression:

an = a1 + ( n - 1 ) d

where

a1 = the initial term

d = the common difference of successive members

an = the nth term

In this case:

a14 = a1 + 13 d = 96

a25 = a1 + 24 d = 173

Now you must solve system:

a1 + 13 d = 96

a1 + 24 d = 173
_____________

Try to solve it.

The solutions are:

a1 = 5 , d = 7