the sum of the first 12 terms of an arithmetic sequence is 144, and the first term is 3.use this formula:an=a1+(n-1)d
Answer (1)
Here's how to solve this problem: 1. Use the formula for the sum of an arithmetic series.[tex] \sf {S_n = \frac{n}{2}[2a_1 + (n-1)d]}[/tex]2. Plug in the given values[tex] \sf {144 = \frac{12}{2}[2(3) + (12-1)d]}[/tex]3. Simplify[tex] \sf {144 = 6[6 + 11d]}[/tex][tex] \sf {24 = 6 + 11d}[/tex][tex] \sf {18 = 11d}[/tex][tex] \sf {d = \frac{18}{11}}[/tex]Final answer:[tex] \sf {d = \frac{18}{11}}[/tex]
