Final answer:
To find the sum of the first five terms of an Arithmetic Progression (A.P.), use the formula: Sum = (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. In this case, the third term is given as 5, which can be used to find the values of a and d. Substitute these values into the formula to calculate the sum.
Step-by-step explanation:
In an Arithmetic Progression (A.P.), the sum of the first five terms can be found using the formula:
Sum = (n/2)(2a + (n-1)d)
Where:
- Sum is the sum of the terms
- n is the number of terms
- a is the first term
- d is the common difference
In this case, the third term is given as 5. Let's denote it as a_3. We can use this information to find the value of a and d. Since a_3 is the third term, we know that a_3 = a + 2d. Substituting the given value of a_3 as 5, we have: 5 = a + 2d.
Now, we can use this equation along with the formula for the sum of the first five terms to find the answer.