Question

There are five terms in an Arithmetic Progression. The sum of these

terms is 55, and the fourth term is five more than the sum of the first

two terms. Find the terms of the Arithmetic progression.​

Answer 1

Given:-

• There are five terms in an Arithmetic Progression.

• $s_{5} = 55$
• the fourth term is five more than the sum of the first two terms.

To Find:-

• terms of the Arithmetic progression.

Solution:-

Let us say the AP is

$a , a + d , a + 2d , a + 3d , a + 4d$

we know that,

$s _{n} = \frac{n}{2} (2a + (n - 1) \times d)$

So,

$s_{5} = \frac{5}{2}(2a + 4d) = 55$

$= > a + 2d = 11..(1)$

Now,

fourth term is five more than the sum of the first two terms.

$= > a + 3d = 5 + a + a + d$

$= > 2d - a = 5..(2)$

Now,

$adding \: equation \: (1) \: and \: (2)$

$a + 2d + 2d - a = 11 + 5$

$= > 4d = 16$

$= > d = 4$

Putting the value of d in equation (1)

$= > a + 2 \times 4 = 11$

$= > a = 3$

So the A.P will be

$3, \: 7, \: 11 \:,15 \:,19$