Determine if the following sequences represent an A.P., assuming that the pattern continues. If it is an A.P., find the nth term:
5, 15, 25, 35, 45, ...
Formula Used.
dn = an + 1 – an
an = a + (n–1)d
In the above sequence,
a = 5;
d1 = a2–a1 = 15–5 = 10
d2 = a3–a2 = 25–15 = 10
d3 = a4–a3 = 35–25 = 10
⇒ As in A.P the difference between the 2 terms is always constant
The difference in sequence is same and comes to be 10.
∴ The above sequence is A.P
The nth term of A.P is an = a + (n–1)d
an = a + (n–1)d = 5 + (n–1)10
= 5 + 10n–10
= –5 + 10n
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