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In an A.P. the first term is 'a' and the common difference is 'd'. If the third term is 5. Fnd the sum of the first five terms of the A.P.​

User Jickson
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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.

User Lionserdar
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