Determine if the following sequences represent an A.P., assuming that the pattern continues. If it is an A.P., find the nth term:
201, 198, 195, 192, ...
Formula Used.
dn = an + 1 – an
an = a + (n–1)d
In the above sequence,
a = 201;
d1 = a2–a1 = 198–201 = –3
d2 = a3–a2 = 195–198 = –3
d3 = a4–a3 = 192–195 = –3
⇒ As in A.P the difference between the 2 terms is always constant
The difference in sequence is same and comes to be (–3).
∴ The above sequence is A.P
The nth term of A.P is an = a + (n–1)d
an = a + (n–1)d = 201 + (n–1)(–3)
= 201–3n + 3
= 204–3n
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