Question Type 5: Finding n or the sum of first n terms when r = 1 Exercises

A geometric sequence has first term $u_1 = 9$ and common ratio $r = 1$. Find the sum of the first $12$ terms, $S_{12}$.

In a geometric series with $u_1 = 9$ and $r = 1$, compute $S_{75}$.

A geometric series has $u_1 = 7.2$ and $r = 1$. Find the sum of the first $40$ terms.

All terms of a geometric sequence are equal to $\tfrac{5}{3}$ (so $r=1$). Find $S_{60}$.

A geometric series has $r=1$ and first term $u_1 = -4$. If $S_n = -124$, find $n$.

A warehouse stacks identical layers of $14$ pallets each. After $n$ layers, the total number of pallets is $350$. Assuming each layer has the same size (so $r=1$), find $n$.

In a geometric series with $u_1 = 9$ and $r = 1$, the sum of the first $n$ terms is $S_n = 234$. Find $n$.

A geometric series has $r=1$ and $u_1 = 2.5$. If $S_n = 80$, find $n$.

A subscription costs a fixed $ $9$ per month. After $n$ months, the total paid is $ $171$. Assuming the monthly cost is constant (so effectively $r=1$), find $n$.

For a geometric series with $r=1$ and $u_1=9$, find the smallest integer $n$ such that $S_n > 1000$.

For a geometric series with common ratio $r=1$, show that $S_n = n\,u_1$.

A geometric series satisfies $r=1$ and $S_n - S_{n-1} = 7$ for $n\ge 2$. Find $S_{100}$.