How many terms of arithmetic sequence 5,79 must be added to get 221
Answers
Answer:
56
,
68
,
70
Step-by-step explanation:
Method 1: Using Arithmetic Sequence Analysis
(I did this version first since the question was asked under "Arithmetic Sequences").
If the initial value,
44
is denoted as
a
0
then we have:
XXX
a
0
=
44
XXX
a
1
=
?
XXX
a
2
=
?
XXX
a
3
=
?
XXX
a
4
=
92
but we know that for an arithmetic sequence with initial value
a
0
and arithmetic increment
d
,
the
n
t
h
value in the sequence is:
XXX
a
n
=
a
0
+
n
⋅
d
XXXXXX
Some will denote the initial value
a
1
;
XXXXXX
in this case the formula becomes:
XXXXXXXXX
a
n
=
a
1
+
(
n
−
1
)
⋅
d
XXXXXX
This seems unnecessarily complicated to me.
so
XXX
a
4
=
92
=
44
+
4
d
XXX
→
d
=
12
and therefore
XXX
a
1
=
44
+
12
=
56
XXX
a
2
=
56
+
12
=
68
XXX
a
3
=
68
+
12
=
80
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Method 2: Just calculate the arithmetic averages
The primary arithmetic mean is the midpoint between
44
and
92
XXX
44
+
92
2
=
68
The arithmetic mean between the initial value and the midpoint is
XXX
44
+
68
2
=
56
The arithmetic mean between the midpoint and the final value is
XXX
68
+
92
2
=
80