Question

The third term of an arithmetic sequence is 25 and the eighth term is 70. What is the first term?

Answer 1

Answer:

7

Step-by-step explanation:

Let the first term be a and the common difference d

Use the formula for the nth term: xn = a + d(n - 1)

The third term = 25 ⇒ x3 = a + d(3 - 1) = 25 ⇒ a + 2d = 25 (1)

The eighth term = 70 ⇒ x8 = a + d(8 - 1) = 70 ⇒ a + 7d = 70 (2)

Subtract (1) from (2)

a + 7d = 70

a + 2d = 25

============ Subtract

    5d = 45

So d = 45 ÷ 5 = 9

Substitute d = 9 into (1) ⇒ a + 2 × 9 = 25 ⇒ a + 18 = 25 ⇒ a = 7

The first term is 7