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The sum of 17 consecutive numbers is 289. The sum of another 10 consecutive numbers, whose first term is 5 more than the average of the first set of consecutive numbers, is:

The sum of 17 consecutive numbers is 289. The sum of another 10 consecutive numbers, whose first term is 5 more than the average of the first set of consecutive numbers, is: Correct Answer 265

Given:

Sum of 17 consecutive numbers = 289

First term of another 10 consecutive numbers is 5 more than the average of 17 consecutive numbers

Formula used:

Average = Sum of all observations/Total number of observations

Sum of A.P. = n/2 × (a + l)

Where A.P. is arithmetic progression, a is first term and l is last term

Calculation:

Average of 17 consecutive numbers = Sum of all numbers/Total numbers

⇒ Average of 17 consecutive numbers = 289/17

⇒ Average of 17 consecutive numbers = 17

First term (a) of another 10 consecutive numbers = 17 + 5 = 22

The numbers are 22, 23, 24, 25, 26, 27, 28, 29, 30, 31

Last term (l) of 10 consecutive numbers = 31

As consecutive numbers are always in A.P.

Sum of 10 numbers = n/2 × (a + l)

⇒ Sum of 10 numbers = 10/2 × (22 + 31)

⇒ Sum of 10 numbers = 5 × 53

∴ Sum of 10 consecutive numbers is 265

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