Question

there are five terms in an ap the sum of these terms is 55 and the fourth term is 5 more than the sum of the first two terms find the terms of a p​

Answer 1

3, 7, 11, 15, 19

Step-by-step explanation:

Given:

• There are 5 terms of A.P
• Sum of 5 terms = 55
• a₄ = a₁+a₂+5

We need to find:

• The five terms of A.P.

Solution:

We know that, usually an A.P is generally in the form of:

⇒ a, a+d, a+2d, a+3d, a+4d

While adding these terms, we get the answer as 55 [Given].

⇒ Sum of 5 terms = 55

⇒ a+a+d+a+2d+a+3d+a+4d = 55

⇒ 5a+10d = 55

⇒ 5(a+2d) = 55

⇒ a+2d = 55/5

⇒ a+2d = 11 ---Eq.(1)

We are also given that,

⇒ a₄ = a₁+a₂+5

⇒ a+(4-1)d = a+a+(2-1)d+5

⇒ a+3d = 2a+d+5

⇒ -a+2d = 5 ---Eq.(2)

Subtracting Eq.(1) from Eq.(2), we get:

⇒ -a+2d-(a+2d) = 5-11

⇒ -a+2d-a-2d = -6

⇒ -2a = -6

⇒ a = -6/-2

⇒ a = 3

Here, we can substitute the value of a in any equation, let's say Eq.(1):

⇒ a+2d = 11

⇒ 3+2d = 11

⇒ 2d = 11-3

⇒ 2d = 8

⇒ d = 8/2

⇒ d = 4

Therefore,

⇒ First term = a = 3

⇒ Second term = a+d = 3+4 = 7

⇒ Third term = a+2d = 3+2(4) = 3+8 = 11

⇒ Fourth Term = a+3d = 3+3(4) = 3+12 = 15

⇒ Fifth Term = a+4d = 3+4(4) = 3+16 = 19

Hence, the A.P is 3,7,11,15,19.