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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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The first term of an arithmetic sequence is 7, its last term is 70, and its sum is 385. Find the number of terms in the sequence and the common difference.

This page covers key problems related to arithmetic and geometric sequences. Learn how to find the number of terms in an arithmetic sequence, determine the sum to infinity for a geometric series, and more. Suitable for high school students (Grades 10-12).

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