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Question

What is the first term in an arithmetic sequence?


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Solution

Arithmetic sequence:

  • The arithmetic progression is a series of numbers in which the difference between any consecutive terms is equal.
  • The first term of a series is the number with which the series begins.
  • It is an important factor in determining the nthterm of the series and also the sum of the given series.
  • The first term is generally represented as "a".
  • The formula to find the nth term of a series is an=a+n-1d,where nis the number of terms, d is the common difference, anis the nth term and ais the first term.
  • The formula for the sum of nterms in an arithmetic series is Sn=n22a+n-1d where nis the number of terms, d is the common difference, and ais the first term.
  • If the first and the nth term of the series are known, The sum is Sn=n2a+an where n is the number of terms, ais the first term, anis the nth term.

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