Determine the first and last terms of an arithmetic series with 50 terms, a common difference of 6, and a sum of 7,850.

The first term is 10 and the 50th term is 304.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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

`S_n=n (a_1+a_n)/2`

Substituting the known values and `a_1+294 " for " a_50` we get the following:

`7,850=50(a_1+a_1+294)/2`
`7,850=25(2a_1+294)`
`314=2a_1+294`
`20=2a_1 ==> a_1=10, a_50=304`

Last Updated by eNotes Editorial on

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial