Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: From Patterns to Generalizations: Sequences and Series, Exercise 53: Chapter review

Write down the first five terms for the recursive sequence $u_n=-2u_{n-1}+3 \text{with} u_1=-4$.

For the geometric series $0.5-0.1+0.02...., S_n=0.416$. Find the number of terms in the series.

For a geometric progression, $u_3=4.5 \text{and} u_7=22.78125$. Find the value of the common ratio and the first term.

Which of the following sequences has an infinite sum Justify your choice and find that sum.

How many terms are in the sequence $4,7,10, ...., 61$?

In a geometric sequence, the fourth term is $8$ times the first term. If the sum of the first $8$ terms is $765$, find the $9\mathrm{th}$ term of the sequence.

Three consecutive terms of a geometric sequence are $x-3, 6 \text{and} x+2$. Find all the possible values of $x$.

The first seven numbers in row $14$ of Pascal's triangle are $1,13,78,286,715,1287,1716$.

Complete the row and explain your strategy.