Answer:
To find the
n
t
h
term, we use the formula
x
n
=
a
+
d
(
n
−
1
)
, where
n
is the term you are looking for,
a
is the
1
s
t
term and
d
is the difference between terms (it does not vary)
From the arithmetic sequence
−
3
,
4
,
11
,
18
...
, we can see that
a
=
−
3
and
d
=
7
You can find
d
by subtracting a number by its precedent
⇒
d
=
4
−
(
−
3
)
=
7
or
d
=
11
−
4
=
7
and so on! It's always going to be the same value.
So,
x
15
=
−
3
+
7
(
15
−
1
)
=
−
3
+
7
(
14
)
=
−
3
+
98
=
95
Another way to do this since it's "only" the
15
t
h
term is by hands or calculator. They already gave you the four terms, which will help you find the difference "
d
". Use only the first term "
−
3
" and add 7 until you reach the
15
t
h
term.
⇒
−
3
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
=
95
Explanation: