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.
OR​

Answer 1

Given :   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.

To find :  terms of the Arithmetic progression.​

Solution:

Let say AP is  

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

Sn = (n/2)(2a + (n-1)d )

Sum of 5 terms

= (5/2)(2a + 4d)  = 55

=> a + 2d  =  11

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

=> a + 3d  = 5 + a + a + d

=>   2d  -  a  = 5

Adding both

=> 4d = 16

=> d  = 4

=> a  = 3

AP

3  ,  7  , 11 ,    15  , 19  

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Answer 2

Answer:

Let the terms in the arithmetic progression be a,a+d,a+2d,a+3d and a+4d .

Given the sum of these terms

=5a+10d=55

Hence a+2d=11

So T3=11 also given t4=5+t1+t2

Hence a+3d=5+a+a+d

So 2d=5+a

Adding a on both sides we get

a+2d=5+2a

But a+2d=t3=11

Hence 11=5+2a

So a=3

Also 2d=5+a hence d=4

Hence the series will be

3,7,11,15,19

Step-by-step explanation:

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