Arithmetic Progression: Finding the 50th Term

This solution explains how to find the 50^th term of the given Arithmetic Progression (AP).

Identify Progression Details

• The sequence provided is an Arithmetic Progression: 3, 8, 13, 18, 23, ........
• The first term ($a$) is 3.
• The common difference ($d$) is found by subtracting any term from its succeeding term:
  • $d = 8 - 3 = 5$
  • $d = 13 - 8 = 5$
  Thus, the common difference is $d=5$.
• We need to calculate the 50^th term, meaning $n=50$.

Apply Arithmetic Progression Formula

The formula for the $n^{th}$ term ($a_n$) of an Arithmetic Progression is:

$a_n = a + (n-1)d$

Calculate the 50th Term

Substitute the known values ($a=3$, $d=5$, $n=50$) into the formula:

• $a_{50} = 3 + (50-1) \times 5$
• $a_{50} = 3 + (49) \times 5$
• $a_{50} = 3 + 245$
• $a_{50} = 248$

Result

Therefore, the 50^th term of the Arithmetic Progression 3, 8, 13, 18, 23, ........ is 248.