The two arithmetic progressions (APs)
AP–I: 8, 11, 14, …
AP–II: 3, 8, 13, … are considered.
Answer the following questions relating to these two sequences.
(i) Write the general term an of each AP in terms of n.
(ii) Find the value of n for which the nth terms of the two APs are equal.
(iii) After the value of n obtained in part (ii), which AP will have the larger individual term? Justify your answer algebraically.
(iv) For values of n less than the one obtained in part (ii), which AP will have the greater sum of the first n terms? Explain briefly without doing full numerical calculations.