Question

there are five terms in an ap sum of there five terms is 55,and the fourth term is five more than the sum of the first two terms. find the terms of the ap.​

Answer 1

Answer:

HERE IS YOUR ANSWER

Step-by-step explanation:

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.)

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● 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

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