Question

(iii) If last term of A.P is 21/2 what is the fourth term from the end. "-1/2" 1/2 3/2 5/2​

Answer 1

Answer:

The fourth term from the end is 15/2

Step-by-step explanation:

Last term of AP, aₙ = 21/2

AP : -1/2, 1/2, 3/2, 5/2...

From the given AP, we can interpret that

First term, a₁ = -1/2

Common difference, d = a₂ - a₁ = 1/2 - (-1/2)

                                      = 1/2 + 1/2 = 1

Now, we need to find 4th term from end, if we reverse the given AP (i.e. if last term of this AP becomes the first term of the new AP, AP')

a'₁ = aₙ  = 21/2

(where a'₁ is the first term of new AP)

d' = -d = -1

(due to reversing the AP)

Now,

By formula,

aₙ = a +(n-1)d

a'₄ = a'₁ + (4-1)d'

a'₄ =  21/2 + 3(-1)

a'₄ = 15/2