Question

If following numbers are in AP : a, 7, b, 23, c, then evaluate : a – 2b + c.

Answer 1

Answer:

0 is the correct answer.

☸Given☸

• a, 7, b, 23, c are in A.P.

To Find:

• Value of a-2b+c

✺Solution✺

We know that,

• If p,q,r,s,t are in A.P.,then p,r,t are also in A.P. because terms at equal intervals in A.P. are in A.P.
• If x,y,z are in A.P., then they will follow the condition x+z=2y.

Now, In the given A.P.

$\longrightarrow$a,b,c are in A.P, since they are at equal intervals

So,

$\longrightarrow\sf{a+c=2b}$

$\longrightarrow\sf{a+c-2b=0}$

$\longrightarrow\sf{\purple{a-2b+c=0}}$

➳Hence, the value of $\bf{a-2b+c}$ is $\bf{\green{0}}$.

Answer 2

Given:

a, 7, b, 23, c are in A.P.

To Find:

Value of a-2b+c

Solution:

$a + c = 2b \\ a + c - 2b = 0 \\ a - 2b + c = 0$