Question

The sum of 2nd and 30th term of arthematic sequence is 50 What is the 16th term?
What is the sum of 2nd and 31th term?​

Answer 1

Answer:

(i) 25          ;  (ii) 50

Step-by-step explanation:

Let the first term and common difference of this AP be 'a' and 'd' respectively.

           Using:   aₙ = a + (n - 1)d

Given, sum of 2nd and 30th term is 50

⇒ a₂ + a₃₀ = 50

⇒ (a + d) + (a + 29d) = 50

⇒ 2a + 30d = 50

⇒ 2(a + 15d) = 50

⇒ a + 15d = 25                 ...(1)

(i):    16th term = a + (16 - 1)d

                = 25                 [from (1)]

(ii):  sum of 2nd and 31st can't be given as there is no possible way to get the exact values of 'a and 'd'.

Moreover if your question 'sum of 1st and 31st term'

        ⇒ a + (a + 30d)

        ⇒ 2a + 30d

        ⇒ 50                [from (1)]