The average of five consecutive numbers is $x$. If the next two numbers are also included, how shall the average vary?

Concept & Formula The average of any consecutive sequence of numbers is exactly its middle value. Adding consecutive numbers to the higher end of the series shifts the middle value by exactly 0.5 per number added. Step-by-Step Solution * Given: The average of 5 consecutive numbers is $x$. * Let the 5 consecutive numbers be $a$, $a+1$, $a+2$, $a+3$, $a+4$. * The average (middle term) of these 5 numbers is $a+2$. Thus, $x = a+2$. * Now, include the next two numbers in the sequence: $a+5$ and $a+6$. * The new series now has 7 consecutive numbers: $a$, $a+1$, $a+2$, $a+3$, $a+4$, $a+5$, $a+6$. * The new average (middle term) of these 7 numbers is $a+3$. * Compare the old and new averages: New Average - Old Average = $(a+3) - (a+2) = 1$. * The overall average has increased by 1. Exam Strategy & Shortcut For consecutive integers, every new number added to the higher end of the sequence increases the overall average by exactly 0.5. Since we are adding 2 new numbers, the average increases by $2 \times 0.5 = 1$. This rule lets you solve the problem in seconds without writing any algebraic variables. Common Pitfall Students often waste time assuming specific arbitrary numbers (like 1, 2, 3, 4, 5) and calculating sums manually. While this method works and proves the concept, it drains precious time during an exam compared to using the standard 0.5 increment rule. Final Answer Therefore, the correct answer is It shall increase by 1.