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Question

Given the following sequence, determine whether it is arithmetic progression or not. If it is an Arithmetic progression, find its general term.
–5, 2, 9, 16, 23, 30, ....

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Solution

In the given sequence, we have:
t1 = –5, t2 = 2, t3 = 9, t4 = 16, t5 = 23 and t6 = 30
Thus, we get:
t2 – t1 = 2 – (–5) = 2 + 5 = 7
t3 – t2 = 9 – 2 = 7
t4 – t3 = 16 – 9 = 7
t5 – t4 = 23 – 16 = 7
t6 – t5 = 30 – 23 = 7

Because the difference between any two consecutive terms is constant, which is 7, the given sequence is an arithmetic progression.
We have:
First term, a = t1 = –5
Common difference, d = 7

We know that the general term of an A.P. is tn = a + (n – 1)d.
Thus, the general term of the given A.P. is:
tn = –5 + (n – 1)7 = –5 + 7n – 7
tn = 7n – 12

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