We are given an arithmetic series with the common difference d=6. The sum of the first 50 terms is 7,850, and we are asked to find the first and 50th terms.
First note that we can find the 50th term if we know the first term:
`a_n=a_1+(n-1)d ==> a_50=a_1+49(6) ==> a_50=a_1+294`
The sum of the fifty terms can be found using the formula
Substituting the known values and `a_1+294 " for " a_50` we get the following:
`20=2a_1 ==> a_1=10, a_50=304`