Mathematics - A 40-year building programme for new houses began in Oldtown in the year 1951 (Year 1) and finished in 1990 (Year 40).

A 40-year building programme for new houses began in Oldtown in the year 1951 (Year 1) and finished in 1990 (Year 40).

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Mathematics Arithmeticprogression Q-A1.NS.21 High-school syllabus questions

Anonymous

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The numbers of houses built each year from an arithmetic sequence with a first term a and common difference [/math]d[/math]. Given that 2400 new houses built in 1960 and 600 new houses built in 1990, find the values of a and d.

Ramanath Parimi (last edited 3 years ago) (Expert, Quality Engineer @Qalaxia)

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Step 1: Note down the given terms, and write their equivalent term in the arithmetic sequence.

EXAMPLE: 18th term = a + (n-1)d = a + (18-1)d = a + 17d

21st term = a + 20d.

Step 2: Equate the given terms with the equivalent terms of the arithmetic sequence. This will from the equations.

EXAMPLE: 18th term of the series is 25. Which means, a + 17d = 25

Step 3: Solve these equations (linear equations) to get the unknown values

RECALL : Solve linear equations [Q-A1.V.2]