Question

Let a1, a2, a3.....a18 are in A.P. and a1 =5. if a1 + a6 + a8 + a11 + a13 + a18 = 180, then the value of a18 is​

Answer 1

Answer:

a18= 55

Step-by-step explanation:

REFER the attachment....

Answer 2

Answer:

The value of a₁₈  = 55

Step-by-step explanation:

Given data  

a₁, a₂, a₃..  a₁₈  are in A.P  

and  first term a₁ = 5

a₁ + a₆ + a₈ + a₁₁ + a₁₃ + a₁₈ = 180  

here we need to find the value of a₁₈

let d be the common difference

⇒ in a A.P nth term = a + (n-1) d  [a = first term, d = common difference]

⇒  a₆  =  5 + (6 - 1)d = 5 + 5d

⇒  a₈  =  5 + (8 - 1)d = 5 + 7d

⇒  a₁₁  =  5 + (11 - 1)d = 5 + 10d

⇒  a₁₃  =  5 + (13 -1)d = 5 + 12d

⇒  a₁₈  =  5 + (18 - 1)d = 5+17d        

from given data

5 + 5 + 5d  + 5 + 7d  + 5 + 10d + 5 + 12d + 5+17d  =  180

⇒  30 + 51d = 180

⇒  51d = 150

⇒  d  =  150 / 51 = 50/ 17

common difference d = 50/17

⇒ a₁₈  = 5 + (18 - 1) (50/17)

          = 5 + 17 (50 / 17)

          = 5 + 50 = 55  

⇒  the value of a₁₈  = 55