Answer to Question #264969 in Algebra for Apex Martins

Question

Find the 7th term of an A.P is 15 and the fourth term is 9. Find the sequence of first term

Answer 1

In an arithmetic progression the formula is

 = a1 + ( n - 1 ) d

where

a₁= the initial term

d = the common difference of successive members is d,

a_n = the nth term

In this case:

a₄ = a₁ + ( 4 - 1 ) d = 15

a₁ + 3 d = 15

a₇ = a1 + ( 7 - 1 ) d = 27

a₁ + 6 d = 27

Now you must solve system:

a₁ + 3 d = 15

a₁ + 6 d = 27

solving simultaneously gives

a₁=3

d= 4

The AP is

3,7,11,15,19,23, 27

The sequence of first term

= a₁ + ( n - 1 ) d

= 3 + (1-1)4

where n= first term

=3