Precalculus 2 Practice ExamTest 3Time: 1.5 hours1. Find the partial fraction decomposition of2. Identify the sequence (in the sum) as arithmetic, geometric, or neither and find the sum:3. Identify the sequence as arithmetic, geometric, or neither and find the sum of the first 25 terms using techniques described in class. Round your answer to two decimal places:4. In an arithmetic sequence, and .Find the formula which describes the nth term of this sequence.Using the formula found, write the first three terms of the sequence.5. Use mathematical induction to prove the given formula for every positive integer n:6. An experiment consists of studying the number of boys and girls in families with exactly 3 children. Let brepresent boys and grepresent girls.Describe the sample space that considers the ordering of the births of the 3 children.Describe the event that the family has exactly 2 girls.7. Consider the expression .