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.
a. (i) Write the general term an of each AP in terms of n.
b. (ii) Find the value of n for which the nth terms of the two APs are equal.
c. (iii) After the value of n obtained in part (ii), which AP will have the larger individual term? Justify your answer algebraically.
d. (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.