Question

there 5 terms in an Ap . the sum of these terms is 55 and the 4th term is more than sum of the first two terms.​

Answer 1

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

___________________

Answer 2

${\huge \underline{\mathfrak\green{hy \:mate}}}$

${\huge{\bf\red{answer :}}}$

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

${\huge{\bf\red{Thanks,}}}$

I hope it's helpful