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Question
Check whether 422 is in the sequence 10, 13, 16, 19, 22, ....
Solution
Given sequence is 10, 13, 16, 19, 22, .....
Here, t1 = 10, t2 = 13, t3 = 16
Now, t2 – t1 = 13 – 10 = 3
And t3 – t2 = 16 – 13 = 3
∵ t2 – t1 = t3 – t2
∴ This sequence is an A.P.
So, First term, a = 10
Common Difference, d = 3
Let 422 be its nth term.
Then, tn = a + (n – 1)d
⇒ 422 = 10 + (n – 1)3
⇒ 422 = 10 + 3n – 3
⇒ 422 = 7 + 3n
⇒ 422 – 7 = 3n
⇒ 415 = 3n
⇒ n = 138.333
However, it is not an integer.
As a result, 422 is not in the specified sequence.
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