Question

) The sum of 2nd term and 30th term of an arithmetic sequence is 50.
What is the sum of 1st term and 31st term of this sequence ?

Answer 1

Answer:

sum of 1st term and 31st term is 50

Step-by-step explanation:

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

                    ∴ aₙ = a + (n - 1)d

Given, 2nd term + 30th term = 50

⇒ a₂ + a₃₀ = 50

⇒ [a + (2 - 1)d] + [a + (30 - 1)d] = 50

⇒ a + d + a + 29d = 50

⇒ 2a + 30d = 50        ...(1)

We need to find the value of sum of 1st term and 31st term.

     ⇒ a + a₃₁

     ⇒ a + (a + 30d)

     ⇒ 2a + 30d

     ⇒ 50                  [from (1)]

Hence, sum of 1st term and 31st term is 50