If the sum of five consecutive positive integers is A, then the sum of

In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median

I.e. Median = A/5 = Mean = Third Integer

First Integer = A/5 - 2
Second Integer = A/5 - 1
Third Integer = A/5
Forth Integer = A/5 + 2
Fifth Integer = A/5 + 2

i.e.
SixthInteger = A/5 + 3
Seventh Integer = A/5 + 4
Eigth Integer = A/5 + 5
Ninth Integer = A/5 + 6
Tenth Integer = A/5 + 7

Now Mean of next 5 Integers = Median = A/5 + 5

i.e. Sum of Next 5 integers = (A/5 + 5)*5 = A+25

Answer: option C

To correct here, fourth integer should be A/5 +1 (not A/5+2)

The sum of five consecutive positive integers is A, next 5 consecutive will gain additional 5*5 = 25, so the sum of the next five consecutive integers in terms of A is: A + 25

Answer: C.

Let the first 5 integers be 1,2,3,4,5 (A = 15)and next 5 integers be 6,7,8,9,10 (sum = 40)
Substitute A = 15 in the option. Only option C will yield 40. ANSWER

We can label each integer as follows:

First integer = x

Second integer = x + 1

Third integer = x + 2

Fourth integer = x + 3

Fifth integer = x + 4

Thus:

A = 5x + 10

A - 10 = 5x

(A - 10)/5 = x

A/5 - 2 = x

We see that the next 5 integers are x + 5, x + 6, x + 7, x + 8, and x + 9.

Since we have an evenly spaced set, sum = average x quantity, and since x = A/5 - 2, we have:

sum = (first term in the set + last term in the set)/2 x quantity

sum = [(A/5 - 2 + 5 + A/5 - 2 + 9)/2] x 5

sum = [(2A/5 + 10)/2] x 5

sum = (A/5 + 5) x 5

sum = A + 25

Alternate solution:

If we let the first integer be x, then the first five integers will be x, x + 1, x + 2, x + 3, and x + 4, and the next five integers will be x + 5, x + 6, x + 7, x + 8, and x + 9. We can see that each of the next five integers is 5 more than its counterpart in the first five integers. Thus, the sum of the next five integers is 5 x 5 = 25 more than the sum of the first five integers. So, if the sum of the first five integers is A, the sum of the next five integers is A + 25.

Answer: C

Since the sum of 5 consecutive integers is A, then next 5 terms will be sum of 5+1,5+2,5+3,5+4,5+5 respectively.
Hence sum of the next five consecutive integers in terms of A is 5*5 + (1+2+3+4+5)=25+A

IMO C is the correct answer.

The sum of five consecutive positive integers is A

Let the consecutive numbers be x, x+1, x+2, x+3, x+4
=> Their sum = A

The sum of the next five consecutive integers in terms of A is:

Now, each of the next five consecutive numbers will be 5 more than the previous 5 numbers

Ex: x + 5 is 5 more than x and so on

=> Sum of next 5 numbers = A + 5*5 = A + 25

So, Answer will be C
Hope it helps!

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