#### The first term of an arithmetic series is a and the common difference is d. The 18th term of the series is 25 and the 21st term of the series is 32.5

Show that a = –7.5 and find the value of d

Anonymous

0

Show that a = –7.5 and find the value of d

Krishna

0

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

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

= a + 17d

21th term = a + 20d

Step 2: Set up equations according to the equivalent terms of arithmetic sequence.

NOTE: Equate the given terms with the equivaent terms of arithmetic sequence. This will form the equations.

EXAMPLE: 18th term = 25

a + 17d = 25.................................(1)

21st term = 32.5

a + 20d = 32.5...............................(2)

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

NOTE: Solve the linear equations

1) Substitution method, 2)Cross-multiplication, 3)Elimination method

Step 4: Compare these values with the given values.