Question

What is the sum of the first 10 terms of the Geometric Serie: 4 + 16 +64+.....+ 4^10

Answer 1

Explanation:
This is a geometric sequence with initial term
1
and common ratio
4
:
a
1
=
1
a
n
=
a
1
⋅
4
n
−
1
=
4
n
−
1
10
∑
n
=
1

4
n
−
1
=
1
3
(
4
−
1
)
10
∑
n
=
1

4
n
−
1
=
1
3
(
4
10
∑
n
=
1

4
n
−
1
−
10
∑
n
=
1

4
n
−
1
)
=
1
3
(
11
∑
n
=
2

4
n
−
1
−
10
∑
n
=
1

4
n
−
1
)
=
1
3
⎛
⎝
4
10
+
10
∑
n
=
2

4
n
−
1
−
1
−
10
∑
n
=
2

4
n
−
1
⎞
⎠
=
1
3
(
4
10
−
1
)
=
1
3
(
2
20
−
1
)
=
1
3
(
1048576
−
1
)
#=1048575/3#
=
349525