Given the first three terms of an arithmetic progression as 2x, x + 4 and 2x - 6 respectively. Find the value of x and then give the first five terms of this arithmetic sequence.

Question

Given the first three terms of an arithmetic progression as

2 x, x + 4 a n d 2 x - 6

respectively. Find the value of x and then give the first five terms of this arithmetic sequence.

Answer 1

Step 1 let

a_{1}, a_{2}, a_{3}, a_{4}, a_{5}

be the terms of A.P with common difference "d" according to question

a_{1} = 2 x

a_{2} = x + 4

a_{3} = 2 x - 6

d = a_{2} - a_{1}

d = x + 4 - 2 x

d = 4 - x

also

d = a_{3} - a_{2}

d = 2 x - 6 - x - 4

d = x - 10

as x - 10 = 4 - x

2 x = 14

x = 7

Step 2

so as a_{1} = 2 x

\Rightarrow a_{1} = 14

a_{2} = a_{1} + d

a_{2} = 14 - 3

a_{2} = 11

a_{3} = a_{2} + d

a_{3} = 11 - 3

a_{3} = 8

a_{4} = a_{3} + d

a_{4} = 8 - 3

a_{4} = 5

a_{5} = 5 - 3

a_{5} = 2

so 14, 11, 8, 5, 2

Want to know more about Polynomial arithmetic?