Question

Question 4
Find a, b and c such that the following numbers are in AP.
a, 7, b, 23 and c.

Answer 1

Given; a, 7, b, 23 and c are in AP.
$\therefore$ 7 - a = b - 7 = 23 - b = c - 23 = Common difference

Taking second and third terms, we get;
b – 7 = 23 – b
$\Rightarrow$ 2b = 30
$\therefore$ b = 15
Taking first and second terms, we get;
7 – a = b - 7
$\Rightarrow$ 7 - a = 15 - 7 [$\because$ b = 15]
$\Rightarrow$ 7 - a = 8
$\therefore$ a = - 1
Taking third and fourth terms, we get;
23 - b = c - 23
$\Rightarrow$ 23 - 15 = c - 23 [$\because$ b = 15]
$\Rightarrow$ 8 = c - 23
$\Rightarrow$ 8 + 23 = c $\Rightarrow$ c = 31
Hence, a = -1, b = 15, c = 31.