Sum of Arithmetic Sequence Formulas
You've got two amazing formulas to find the sum of arithmetic sequences, and both will get you the same answer! The first formula is sn=2n(a1+an), which uses the first and last terms. The second formula is sn=2n[2a1+(n−1)d], which uses the first term and common difference.
Let's see how this works with the sequence 17, 22, 27, 32... where we want the first 25 terms. Here, a1=17, d=5, and n=25.
Using the second formula: s25=225[2(17)+(25−1)5]=225[34+120]=225[154]=1925. You can double-check this by finding a25=137 first, then using the first formula to get the same result!
Quick Tip: Choose the formula based on what information you're given - if you know the last term, use the first formula; if you know the common difference, use the second!