Question

Sum of first and 25th terms of an arithmetic sequence is 70.
(ii) What is the 13th term of this sequence ?

Hint:

Notice that the 13th term is the middle term of the sequence from a₁ to a₂₅. The average of the first and last term in an AP segment gives the value of the middle term. So, a₁₃ = a₁ + a₂₅2 = (70)/(2) = 35.

Answer 1

Using the same AP where a₁ + a₂₅ = 70, we need to find the 13th term (a₁₃).

From the previous part, we established that a₁ + a₂₅ = 2a + 24d = 70.
The 13th term is given by the formula a₁₃ = a + (13-1)d = a + 12d.
We can relate these two expressions.

We have the equation from the given information:
a₁ + a₂₅ = 70 2a + 24d = 70 We can factor out a 2 from the left side of the equation:
2(a + 12d) = 70 Now, divide both sides by 2:
a + 12d = (70)/(2) = 35 The expression for the 13th term is a₁₃ = a + 12d.
Therefore, a₁₃ = 35.

The 13th term of the sequence is 35.