Find the lowest number in an AP such that the sum of all the terms is

1.	Find the lowest number in an AP such that the sum of all the terms is 105 and greatest term is 6 times the least. (a) 5 (b) 10 (c) 15 (d) (a), (b) & (c)
Answer» Correct option (a) 5 Explanation: We get least term 5 and largest term 30 (since the largest term is 6 times the least term). The average of the A.P becomes (5 + 30)/2 = 17.5 Thus, 17.5 × n = 105 gives us: to get a total of 105 we need n = 6 i.e. 6 terms in this A.P. That means the A.P. should look like: 5, _, _, _, _, 30. It can be easily seen that the common difference should be 5. The A.P, 5, 10, 15, 20, 25, 30 fits the situation. The same process used for option (b) gives us the A.P. 10, 35, 60. (10 + 35 + 60 = 105) and in the third option 15, 90 (15 + 90 = 105) Hence, all the three options are correct.

Find the lowest number in an AP such that the sum of all the terms is 105 and greatest term is 6 times the least. (a) 5 (b) 10 (c) 15 (d) (a), (b) & (c)

Answer»

Correct option (a) 5

Explanation:

We get least term 5 and largest term 30 (since the largest term is 6 times the least term).

The average of the A.P becomes (5 + 30)/2 = 17.5 Thus, 17.5 × n = 105 gives us: to get a total of 105 we need n = 6 i.e. 6 terms in this A.P. That means the A.P. should look like: 5, _, _, _, _, 30.

It can be easily seen that the common difference should be 5. The A.P, 5, 10, 15, 20, 25, 30 fits the situation.

The same process used for option (b) gives us the A.P. 10, 35, 60. (10 + 35 + 60 = 105) and in the third option 15, 90 (15 + 90 = 105)

Hence, all the three options are correct.

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