The average of 5 terms is 10, while the average of the first two terms is 7 and the last two terms is 13. What is the value of the third term?

To find the value of the third term, let's break down the information provided step by step.

The average of five terms is 10, which means the total sum of these five terms is:

Total sum = Average × Number of terms = 10 × 5 = 50.

We can denote the five terms as ( a_1, a_2, a_3, a_4, a_5 ). Therefore,

( a_1 + a_2 + a_3 + a_4 + a_5 = 50 ).

Next, the average of the first two terms is 7:

This implies that:

( a_1 + a_2 = 7 × 2 = 14 ).

Similarly, the average of the last two terms is 13:

This gives us:

( a_4 + a_5 = 13 × 2 = 26 ).

Now, we can substitute these sums back into the equation for the total sum:

( 14 + a_3 + 26 = 50 ).

Combining like terms, we have:

( a_3 + 40 = 50 ).

To find ( a_3 ), we simply subtract 40 from