the sum of the first 20 terms of an arithmetic sequence is 400. if first term is 5, find the common difference.
Answer (1)
In the given problem, the common difference is 2To solve this, let's follow the formula for finite numbers[tex]s_n=\frac{n}{2}[2a+(n-1) d][/tex]Substitute for the given values[tex]s_2_0= \frac{20}{2} [2(5)+(20-1)d][/tex]Simplify[tex]400=10 [10+(19)d][/tex]400 = 10 (10+19d)400 = 20+ 190dTranspose 20 to become -20400 - 20 = 190d380 - 190dDivide both sides by 190 so d will be left[tex]\frac{380}{90} =\frac{90d}{90}[/tex]2 = dor by symmetric property,d=2Therefore, the common difference is 2
