Question

The second, fourth and sixth terms of an AP are x-1, x+1, and 7 respectively. Find the common difference, first term and the value of x

Answer 1

Answer:

common difference = 0

first term = -7

value of x = -6

Answer 2

Step-by-step Explanation:

.

$\sf {a}_{2} = x - 1 \: \: \: ...(given)$

$\sf {a}_{4} = x + 1 \: \: \: ...(given)$

$\sf {a}_{6} =7 \: \: \: \: \: \: \: \: \: \: ...(given)$

$\implies\sf {a}_{n} = a + (n - 1)d$

$\implies\sf {a}_{2} = a + (2 - 1)d$

$\implies\sf x - 1 = a +d \: \: \: ...(1)$

$\implies\sf {a}_{4} = a + (4 - 1)d$

$\implies\sf x + 1 = a + 3d \: \: \: ...(2)$

$\implies\sf {a}_{6} =a + (6 - 1)d$

$\implies\sf 7 =a + 5d \: \: \: ...(3)$

$Substract \: Eq \: [1] \: from \: Eq \: [2],$

$\implies\sf x + 1 - (x - 1) = a + 3d - (a + d)$

$\implies\sf x + 1 - x + 1 = a + 3d - a - d$

$\implies\sf 2 = 2d$

$\implies\bf d = 1$

$Substituting \: this \: value \: of \: d \: in \: Eq \: [3],$

$\implies\sf 7 =a + 5d \: \: \: ...(3)$

$\implies\sf 7 =a + 5(1)$

$\implies\sf 7 =a + 5$

$\implies\bf a = 2$

$Substituting \: this \: value \: of \: a \And d \: in \: Eq \: [1 ] ,$

$\implies\sf x - 1 = a +d \: \: \: ...(1)$

$\implies\sf x - 1 =2 +1$

$\implies\sf x =3 + 1$

$\implies\bf x =4$

REQUIRED ANSWER,

.

• The common difference is 1.
• The first term is 2.
• The value of x is 4.