Determine if the following sequences represent an A.P., assuming that the pattern continues. If it is an A.P., find the nth term:
1, 11, 111, 1111, ...
Formula Used.
dn = an + 1 – an
In the above sequence,
a = 1;
d1 = a2–a1 = 11–1 = 10
d2 = a3–a2 = 111–11 = 100
d3 = a4–a3 = 1111–111 = 1000
⇒ As in A.P the difference between the 2 terms is always constant
But the difference in sequence is not the same.
∴ The above sequence is not A.P
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