Questions: Find the sum of the first 25 terms of the arithmetic sequence. a1=100 and a25=220

Solution Steps

To find the sum of the first 25 terms of an arithmetic sequence, we can use the formula for the sum of an arithmetic sequence: \( S_n = \frac{n}{2} \times (a_1 + a_n) \), where \( n \) is the number of terms, \( a_1 \) is the first term, and \( a_n \) is the last term. Here, \( n = 25 \), \( a_1 = 100 \), and \( a_{25} = 220 \).

We are given the first term \( a_1 = 100 \) and the 25th term \( a_{25} = 220 \) of the arithmetic sequence. The number of terms \( n \) is \( 25 \).

To find the sum \( S_n \) of the first \( n \) terms of the arithmetic sequence, we use the formula: \[ S_n = \frac{n}{2} \times (a_1 + a_n) \] Substituting the known values: \[ S_{25} = \frac{25}{2} \times (100 + 220) \]

Calculating the expression: \[ S_{25} = \frac{25}{2} \times 320 = 25 \times 160 = 4000 \]

Final Answer