Question

There are five terms in A.P. The sum of these terms is 55 and the fourth term is five more than the sum of the first two terms. Find the of the A.P.

Answer 1

Given :-

• There are 5 terms in AP
• Sum of these terms is 55
• a₄ = a₁ + a₂ + 5

To find :-

• To find the AP

Solution :-

Let, 5 terms in AP be

first term = a-2d ,

second term =  a-d ,

third term = a ,

fourth term =a+d ,

fifth term =  a+2d

then,

⇢  sum of all terms = 55

⇢  a-2d+a-d+a+a+d+a+2d = 55

⇢  5 a = 55

⇢ a = 11  

Also,

⇢ a₄ = a₁ + a₂ + 5

⇢ a + d = a - 2 d + a - d + 5

⇢ a - 2a + d + 3 d  = 5

⇢   4 d - 11 = 5

⇢ 4 d = 16

⇢ d = 4

So the five terms will be

⇨   a - 2 d = 11 - 2(4) = 3

⇨   a - d = 11 - 4 = 7

⇨   a = 11

⇨   a + d = 11 + 4 = 15

⇨   a + 2 d = 11 + 2 (4) = 19

Required AP will be

3 , 7 , 11 , 15 , 19 .

(Ans.)

_________________________

● In this type of question the most important part is about selection of terms

selecting 3 consecutive terms of AP

a - d , a , a + d

selecting 4 consecutive terms of AP

a - 3 d , a - d , a + d , a + 3 d

selecting 5 consecutive terms in AP

a - 2 d , a - d , a , a + d , a + 2 d

selecting 6 consecutive terms in AP

a - 5 d , a - 3 d , a - d , a +d , a + 3 d + a + 5 d

___________________

Answer 2

Answer:

Given :-

There are 5 terms in AP

Sum of these terms is 55

a₄ = a₁ + a₂ + 5

To find :-

To find the AP

Solution :-

Let, 5 terms in AP be

first term = a-2d ,

second term =  a-d ,

third term = a ,

fourth term =a+d ,

fifth term =  a+2d

then,

⇢  sum of all terms = 55

⇢  a-2d+a-d+a+a+d+a+2d = 55

⇢  5 a = 55

⇢ a = 11  

Also,

⇢ a₄ = a₁ + a₂ + 5

⇢ a + d = a - 2 d + a - d + 5

⇢ a - 2a + d + 3 d  = 5

⇢   4 d - 11 = 5

⇢ 4 d = 16

⇢ d = 4

So the five terms will be

⇨   a - 2 d = 11 - 2(4) = 3

⇨   a - d = 11 - 4 = 7

⇨   a = 11

⇨   a + d = 11 + 4 = 15

⇨   a + 2 d = 11 + 2 (4) = 19

Required AP will be

3 , 7 , 11 , 15 , 19 .

(Ans.)

_________________________

● In this type of question the most important part is about selection of terms

selecting 3 consecutive terms of AP

a - d , a , a + d

selecting 4 consecutive terms of AP

a - 3 d , a - d , a + d , a + 3 d

selecting 5 consecutive terms in AP

a - 2 d , a - d , a , a + d , a + 2 d

selecting 6 consecutive terms in AP

a - 5 d , a - 3 d , a - d , a +d , a + 3 d + a + 5 d

___________________