Arithmetic Series: Find 1st 3 Terms & 20th Term

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SUMMARY

The nth term of the arithmetic series is defined as 1/2(3-n). To find the first three terms, substitute n with 1, 2, and 3, resulting in the terms 1, 0, and -1 respectively. The 20th term is calculated by substituting n with 20, yielding -8. This method effectively utilizes the formula for the nth term of an arithmetic series, which is a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

PREREQUISITES
  • Understanding of arithmetic series and sequences
  • Familiarity with the nth term formula: nth term = a + (n-1)d
  • Basic algebra for substitution and solving equations
  • Knowledge of term indexing in sequences
NEXT STEPS
  • Study the derivation and applications of the nth term formula in arithmetic sequences
  • Explore examples of finding terms in geometric series for comparison
  • Learn about the implications of common differences in arithmetic series
  • Practice solving problems involving arithmetic series with varying initial conditions
USEFUL FOR

Students studying algebra, educators teaching arithmetic sequences, and anyone looking to enhance their problem-solving skills in mathematics.

kwuk
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Homework Statement



The nth term of an arithmetic series is 1/2(3-n). What are the first three terms and the 20th term?


Homework Equations



nth term = a+(n-1)d

The Attempt at a Solution



I have made various attempts but cannot seem to work out how this can be done without a specific number for n. Have answered questions where two different terms have been given and used simultaneous equations to determine the first term and common difference but can't seem to do this as only one term is given. Advice anyone??
 
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kwuk said:
The nth term of an arithmetic series is 1/2(3-n). What are the first three terms and the 20th term?

Hi kwuk! :smile:

(i assume you mean (3-n)/2)

erm :redface: … the first three terms have n = 1, 2, 3, and the 20th has n = 20 :wink:
 

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