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Question

(i) Which term of the A.P. 3, 8, 13, ... is 248?
(ii) Which term of the A.P. 84, 80, 76, ... is 0?
(iii) Which term of the A.P. 4, 9, 14, ... is 254?

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Solution

(i) 3, 8, 13...
Here, we have:
a = 3
d = 8-3 =5
Let an = 248 a+n-1d = 2483+n-15 = 248n-15 =245n-1 = 49 n= 50

Hence, 248 is the 50th term of the given A.P.

(ii) 84, 80, 76...
Here, we have:
a = 84
d = 80-84 = -4
Let an =0a+(n-1)d = 084 + (n-1)-4 = 0 (n-1)-4 = -84(n-1) = 21 n = 22

Hence, 0 is the 22nd term of the given A.P.

(iii) 4, 9, 14...
Here, we have:
a = 4
d = 9-4 = 5
Let an = 254a+n-1 d = 2544+n-1 5 = 254n-1 5 =250n-1 = 50 n= 51

Hence, 254 is the 51st term of the given A.P.

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