Determine if the following sequences represent an A.P., assuming that the pattern continues. If it is an A.P., find the nth term:
17, 22, 27, 32, ...
Formula Used.
dn = an + 1 – an
an = a + (n–1)d
In the above sequence,
a = 17;
d1 = a2–a1 = 22–17 = 5
d2 = a3–a2 = 27–22 = 5
d3 = a4–a3 = 32–27 = 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 = 17 + (n–1)5
= 17 + 5n–5
= 12 + 5n
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