How many terms are identical in the two A.P.s 21, 23, 25,... up to 120

1.	How many terms are identical in the two A.P.s 21, 23, 25,... up to 120 terms and 23, 26, 29,... up to 80 terms? (a) 39 (b) 40 (c) 41 (d) None of these.
Answer» Correct option (b) 40 Explanation: The first common term is 23, the next will be 29 (Notice that the second common term is exactly 6 away from the first common term. 6 is also the LCM of 2 and 3 which are the respective common differences of the two series.) Thus, the common terms will be given by the A.P 23, 29, 35 ....., last term. To find the answer you need to find the last term that will be common to the two series. The first series is 23, 25, 27 ... 259 While the second series is 23, 26, 29 ..... 260. Hence, the last common term is 257 Thus our answer becomes [(257 -23)/6]+1 =40.

How many terms are identical in the two A.P.s 21, 23, 25,... up to 120 terms and 23, 26, 29,... up to 80 terms? (a) 39 (b) 40 (c) 41 (d) None of these.

Answer»

Correct option (b) 40

Explanation:

The first common term is 23, the next will be 29 (Notice that the second common term is exactly 6 away from the first common term. 6 is also the LCM of 2 and 3 which are the respective common differences of the two series.)

Thus, the common terms will be given by the A.P 23, 29, 35 ....., last term. To find the answer you need to find the last term that will be common to the two series.

The first series is 23, 25, 27 ... 259

While the second series is 23, 26, 29 ..... 260.

Hence, the last common term is 257

Thus our answer becomes [(257 -23)/6]+1 =40.

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