Determine the ap whose third term is 16 and the 7th term exceeds the 5th term by 12

General
1

determine the ap whose third term is 16 and the 7th term exceeds the 5th term by 12

2

Determine the arithmetic progression (AP)

Answer:
To determine the arithmetic progression (AP) based on the given information that the third term is 16 and the 7th term exceeds the 5th term by 12, we need to follow these steps:

Let the first term of the AP be ‘a’ and the common difference be ‘d’.
The nth term of an AP can be calculated using the formula:
[ a_n = a + (n-1)d ]

Given data:

  • The third term is 16, so ( a + 2d = 16 )
  • The 7th term exceeds the 5th term by 12, so ( a + 6d = a + 4d + 12 ) or ( a + 6d = a + 4d + 12 )
    Simplifying, we get:
    ( 2d = 16 \rightarrow d = 8 )
    ( 2d = 12 \rightarrow d = 6 )

Now, we have found that the common difference is 8 and 6 according to the two equations. This inconsistency means that the given data leads to different common differences, which makes it invalid. The AP cannot be determined with the provided information.