Answer:
This is a geometric series with r = 3. First, find what term
10935
is.
5
⋅
(
3
n
−
1
)
=
10935
(
3
n
−
1
)
=
2187
3
n
−
1
=
3
7
n
−
1
=
7
n
=
8
Now use the formula for the sum of the first
n
terms of a geometric series:
S
n
=
a
1
(
1
−
r
n
)
1
−
r
S
8
=
5
(
1
−
3
8
)
1
−
3
=
16400
Step-by-step explanation:
Explanation:
Step 1: Classify the sequence
Since
t
2
=
3
t
1
and
t
3
=
3
t
2
, this sequence is geometric with
r
=
3
.
Step 2: Find the number of terms
There is no formula we can use to evaluate the sum without knowing the number of terms. By the formula
t
n
=
a
(
r
)
n
−
1
, we have:
10935
=
5
(
3
)
n
−
1
2187
=
3
n
−
1
3
7
=
3
n
−
1
7
=
n
−
1
n
=
8
Step 3: Evaluate the sum
The formula for the sum of a geometric series is
s
n
=
a
(
1
−
r
n
)
1
−
r
.
s
8
=
5
(
1
−
3
8
)
1
−
3
s
8
=
−
32800
−
2
s
8
=
16
,
400
Practice Exercises
1
. Find the sum:
2
+
8
+
32
+
128
+
...
+
524
,
288
Solution
1
.
699
,
050
Hopefully this helps!
