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Let’s check out your problem:
If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
=
(
a
n
−
1
)
2
+
n
a_{n}=\left(a_{n-1}\right)^{2}+n
a
n
=
(
a
n
−
1
)
2
+
n
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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Math Problems
Algebra 2
Evaluate expression when a complex numbers and a variable term is given
Full solution
Q.
If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
=
(
a
n
−
1
)
2
+
n
a_{n}=\left(a_{n-1}\right)^{2}+n
a
n
=
(
a
n
−
1
)
2
+
n
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Find
a
2
a_{2}
a
2
:
Given
a
1
=
4
a_{1} = 4
a
1
=
4
, we need to find
a
4
a_{4}
a
4
using the recursive formula
a
n
=
(
a
n
−
1
)
2
+
n
a_{n} = (a_{n-1})^2 + n
a
n
=
(
a
n
−
1
)
2
+
n
. We will start by finding
a
2
a_{2}
a
2
.
\newline
a
2
=
(
a
1
)
2
+
2
a_{2} = (a_{1})^2 + 2
a
2
=
(
a
1
)
2
+
2
\newline
=
(
4
)
2
+
2
\quad = (4)^2 + 2
=
(
4
)
2
+
2
\newline
=
16
+
2
\quad = 16 + 2
=
16
+
2
\newline
=
18
\quad = 18
=
18
Find
a
3
a_{3}
a
3
:
Now we will find
a
3
a_{3}
a
3
using
a
2
a_{2}
a
2
.
\newline
a
3
=
(
a
2
)
2
+
3
=
(
18
)
2
+
3
=
324
+
3
=
327
a_{3} = (a_{2})^2 + 3 = (18)^2 + 3 = 324 + 3 = 327
a
3
=
(
a
2
)
2
+
3
=
(
18
)
2
+
3
=
324
+
3
=
327
Find
a
4
a_{4}
a
4
:
Finally, we will find
a
4
a_{4}
a
4
using
a
3
a_{3}
a
3
.
\newline
a
4
=
(
a
3
)
2
+
4
=
(
327
)
2
+
4
=
106929
+
4
=
106933
a_{4} = (a_{3})^2 + 4 = (327)^2 + 4 = 106929 + 4 = 106933
a
4
=
(
a
3
)
2
+
4
=
(
327
)
2
+
4
=
106929
+
4
=
106933
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b
b
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