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Sequences & Series · Part 2 of 2
6 exam-style questions with model answers, plus 8 quick multi-choice questions — every question on this part of the standard, grouped by the 2 pages of notes they come from.
Write a full answer before you reveal the model one. That comparison is where the learning happens.
Find the general term and the 9th term of the geometric sequence
A ball is dropped from 3 m and rebounds to 65% of its previous height each bounce. Find the height after the 6th bounce, and find the first bounce after which the ball rises less than 20 cm.
The 2nd, 4th and 7th terms of an arithmetic sequence are also, in that order, the 1st, 2nd and 3rd terms of a geometric sequence. Given the arithmetic sequence has first term 4, find its common difference and the common ratio of the geometric sequence.
Find the sum to infinity of the geometric series
A geometric series has first term 40 and sum to infinity 250. Find the common ratio and the sum of the first 6 terms.
A geometric series has second term 6 and sum to infinity 32. Find all possible values of the first term and the common ratio, and explain why one apparent solution must be rejected.