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

In an Arithmetic Progression (A.P.), the nth term can be expressed as a + (n-1)d, where a is the first term and d is the common difference.

Given that a1 = 5, we can express the other terms as follows:

a6 = a1 + 5d = 5 + 5d a8 = a1 + 7d = 5 + 7d a11 = a1 + 10d = 5 + 10d a13 = a1 + 12d = 5 + 12d a18 = a1 + 17d = 5 + 17d

We are given that a1 + a6 + a8 + a11 + a13 + a18 = 180, so we can substitute the above expressions into this equation:

5 + (5 + 5d) + (5 + 7d) + (5 + 10d) + (5 + 12d) + (5 + 17d) = 180 30 + 51d = 180 51d = 150 d = 150 / 51 = 50 / 17

Substituting d = 50 / 17 into the expression for a18 gives:

a18 = 5 + 17 * (50 / 17) = 5 + 50 = 55

So, the value of a18 is 55.