Show that a1, a2, \dots, an, \dots form an AP where an is defined as below: (i) an = 3 + 4n (ii) an = 9 - 5n Also find the sum of the first 15 terms in each case.

Question

Show that $a_1, a_2, \dots, a_n, \dots$ form an AP where $a_n$ is defined as below:
(i) $a_n = 3 + 4n$
(ii) $a_n = 9 - 5n$

Also find the sum of the first 15 terms in each case.

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