Determine if the following sequences represent an A.P., assuming that the pattern continues. If it is an A.P., find the nth term:
101, 99, 97, 95, ...
Formula Used.
dn = an + 1 – an
an = a + (n–1)d
In the above sequence,
a = 101;
d1 = a2–a1 = 99–101 = –2
d2 = a3–a2 = 97–99 = –2
d3 = a4–a3 = 95–97 = –2
⇒ As in A.P the difference between the 2 terms is always constant
The difference in sequence is same and comes to be (–2).
∴ The above sequence is A.P
The nth term of A.P is an = a + (n–1)d
an = a + (n–1)d = 101 + (n–1)(–2)
= 101–2n + 2
= 103–2n
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