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Assignment Questions Overview

(1) Arithmetic and Geometric Series:

• (a) Find the number of terms in an arithmetic sequence given its first term and the sum.
• (b) Determine the values of $x$ for which a geometric series converges and find a specific value of $x$ for which the sum to infinity is given.
• (c) Find the first term and the common difference of an arithmetic sequence based on a relationship involving another sequence.

(2) Sequence Summation:

• (i) Find a general term $u_n$ in terms of $n$.
• (ii) Find $u_{n+1}$ in terms of $u_n$.

(3) Sequence Definition and Analysis:

• (i) Evaluate specific terms of a sequence.
• (ii) Find the ratio of consecutive terms for a geometric check.
• (iii) Find the sum of the sequence's terms.

(4) Series and Summation:

• (i) Find a constant $C$ using a given expression.
• (ii) Compute the sum of a particular sequence expression.

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