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The sum of 7 consecutive the positive integers is equal to the

Question

The sum of $7$ consecutive the positive integers is equal to the sum of the next five consecutive integers. What is the largest among the $12$ numbers?

24

23

22

21

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The sum of

7

consecutive the positive integers is equal to the sum of the next five consecutive integers. What is the largest among the

12

numbers?

14 mins ago

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14 mins ago

Text solutionVerified

Sum of

7

consecutive terms

S_{n} = \frac{7}{2} [2 a + 6] (d = 1)

Sum of next

5

terms

S_{n} = \frac{5}{2} [2 (a + 7 d) + 4 d] S^{'}_{n} = 5 (a + 9)

S_{n} = S_{n}^{'} 7 (a + 3) = 5 (a + 9) 2 a = 45 - 21 = 24 (a = 12)

The AP is:

12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23

Largest is

23

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Question Text	The sum of $7$ consecutive the positive integers is equal to the sum of the next five consecutive integers. What is the largest among the $12$ numbers?
Answer Type	Text solution:1
Upvotes	150