Answer to Question #237133 in Algebra for Mr. Lee

Question

Determine the sum of the progression if there are 7

arithmetic mean between 3 and 35.

Answer 1

Let the 7 arithmetic mean between 3 and 35 are a + d, a + 2d, ,,,, , a + 7d.

Hence, the arithmetic progression will be a = 3, a + d, a + 2d,...,a+7d, a + 8d = 35.

Since, a + 8d = 35 and a = 3.

Hence, 3 + 8d = 35 => d = 4

So, required sum = (a + d) + (a + 2d) +.... + (a + 7d)

= 7a + (1+ 2 +...+ 7) d

= 7a + 28d

= 7×3 + 28×4

= 133