20th term from the last term of arithmetic sequence \( 3,8,13, \ldots \ldots \ldots, 253 \) is .................... 151 158

To find the 20th term from the last term of the arithmetic sequence \(3, 8, 13, \ldots, 253\), we first need to identify the common difference and the total number of terms in the sequence. 1. **Identify the common difference**: The common difference \(d\) can be calculated as: \[ d = 8 - 3 = 5 \] 2. **Identify the first term and the last term**: The first term \(a\) is \(3\) and the last term \(l\) is \(253\). 3. **Find the number of terms \(n\)**: The formula for the \(n\)-th term of an arithmetic sequence is given by: \[ l = a + (n-1)d \] Plugging in the known values: \[ 253 = 3 + (n-1) \cdot 5 \] Rearranging gives: \[ 253 - 3 = (n-1) \cdot 5 \] \[ 250 = (n-1) \cdot 5 \] \[ n-1 = \frac{250}{5} = 50 \] \[ n = 50 + 1 = 51 \] 4. **Find the 20th term from the last term**: The 20th term from the last term can be found by calculating: \[ \text{20th term from last} = l - (20-1)d \] Substituting the values: \[ \text{20th term from last} = 253 - 19 \cdot 5 \] \[ = 253 - 95 \] \[ = 158 \] Thus, the 20th term from the last term of the arithmetic sequence is \(158\).