Determine if the following sequences represent an A.P., assuming that the pattern continues. If it is an A.P., find the nth term:
Natural numbers which are multiples of 3 or 5 in increasing order.
Formula Used.
dn = an + 1 – an
an = a + (n–1)d
The sequence of natural numbers which are multiple of 3 or 5
in increasing order
Is 3, 5, 6, 9, 10 ……
In the above sequence,
a = 3;
d1 = a2–a1 = 5–3 = 2
d2 = a3–a2 = 6–5 = 1
d3 = a4–a3 = 9–6 = 3
⇒ As in A.P the difference between the 2 terms is always constant
The difference in sequence is not same .
∴ The above sequence is not A.P
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