Find the 12th term from the end of the following arithmetic progressions:

Question:

Find the 12th term from the end of the following arithmetic progressions:

(i) 3, 5, 7, 9, ... 201

(ii) 3, 8, 13, ..., 253

(iii) 1, 4, 7, 10, ..., 88

Solution:

(i) 3, 5, 7, 9...201

Consider the given progression with 201 as the first term  and −2 as the common difference.

12th term from the end $=201+(12-1)(-2)=179$

(ii) 3, 8, 13...253

Consider the given progression with 253 as the first term  and −5 as the common difference.

12th term from the end $=253+(12-1)(-5)=198$

(iii) 1, 4, 7, 10...88

Consider the given progression with 88 as the first term and −3 as the common difference.

12th term from the end $=88+(12-1)(-3)=55$

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