Question

Find the three terms of an AP in when the sum of first two term is10 and Sum of last two terms
is 16​

Answer 1

Given,

For an Arithmetic Progression;

Total number of terms = 3

The sum of the first two terms = 10

The sum of the last two terms = 16

To find,

The three terms of the A.P.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

For an A.P. with the first term a and common difference d, its n-th term can be represented as;

n-th term of the A.P.= An = a + (n-1)d

So, for the given A.P.,

The first term = a

Second term (second last term) = a + d

Third term (last term) = a + 2d

Now, according to the question;

First-term + last term = 10

=> a + (a + d) = 10

=> 2a + d = 10

{Equation-1}

Also,

Second last term + Last term = 16

=> (a + d) + (a + 2d) = 16

=> 2a + 3d = 16

{Equation-2}

Now, by subtracting equation-1 from equation-2, we get;

{2a + 3d} - {2a + d} = 16

=> 3d - d = 6

=> 2d = 6

=> d = 3

Now, by substituting the value of d in equation-1, we get;

2a + d = 10

=> 2a + 3 = 10

=> 2a = 7

=> a = 3.5

So, the first term = a = 3.5

Second term = a + d = 3.5 + 3 = 6.5

Third term = a + 2d = 3.5 + 2×3 = 9.5

Hence, the three successive terms of the A.P. are 3.6, 6.5, and 9.5, respectively.