Question

let a,b,c are three consecutive terms of an arithmetic sequence which is true ?
a) a+c=b
b)a+c/2=b
c)a+c/4=b
d)a+c=b/2​

Answer 1

Answer:

b

Step-by-step explanation:

if we take a= 1,b=2and c=3 then

1+3=4/2=2

Answer 2

In given options, option (b) a+c/2 = b is true

GIVEN :

a,b,c are three consecutive terms of an arithmetic sequence

TO FIND :

which is true from options

a) a+c=b        b)a+c/2=b           c)a+c/4=b           d)a+c=b/2​

SOLUTION :

Given a, b, c are in AP

Lets remember a few points about Arithmetic Progression

Arithmetic Progression

• A sequence of numbers in which the difference between any two consecutive numbers is a constant value is called as Arithmetic Progression

• For example, The series of natural numbers: 1, 2, 3, 4,…  with common difference 1  

• In above series the difference between any two terms will be same like 2 - 1 = 1, 3 - 2 = 1, 4-3 = 1 and so on.

Given that a, b and c are in AP

Here, term 1 = a, term 2 = b and term 3 = c

As we know term 2 - term 1 = term 3 - term 2  

⇒ b - a = c - b

⇒ b + b = a + c

⇒ 2b = a + c

⇒ b = (a+c)/2

Therefore,

In given options, option (b)a+c/2 = b is true

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