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 consecutive multiples of 5 in increasing order.
Formula Used.
dn = an + 1 – an
an = a + (n–1)d
The sequence of natural numbers which are consecutive multiples of 5
Is 5, 10, 15, 20 ……
In the above sequence,
a = 5;
d1 = a2–a1 = 10–5 = 5
d2 = a3–a2 = 15–10 = 5
d3 = a4–a3 = 20–15 = 5
⇒ As in A.P the difference between the 2 terms is always constant
The difference in sequence is same and comes to be 5.
∴ 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)5
= 5 + 5n–5
= 5n
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