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Question

(i) Is 68 a term of the A.P. 7, 10, 13, ...?
(ii) Is 302 a term of the A.P. 3, 8, 13, ...?

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Solution

(i) 7, 10, 13...
Here, we have:
a = 7
d = 10-7 = 3Let an = 68 a+(n-1) d = 687+(n-1)(3) = 68(n-1)(3) = 61(n-1) = 613n = 613 +1 = 643

Since n is not a natural number.So, 68 is not a term of the given A.P.

(ii) 3, 8, 13...
Here, we have:
a = 3
d = 8-3=5Let an = 302 a+n-1d = 3023+n-15 = 302n-15 =299n-1 = 2995n = 2995+1 = 3045
Since n is not a natural number.So, 302 is not a term of the given A.P.

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