Question

For which value of m, 10,m,-2 will be

in A.P.

(a) 4 (b) 3 (c) 2 (d) 1​

Answer 1

Answer :

$\large\boxed{\bf{(a.)\:m\:=\:4}}$

Correct Question :–

For which value of 10 , m , (-2) will be  in A.P.

(a) 4 (b) 3 (c) 2 (d) 1​

Explanation :

Given :–

• A.P.  :- 10 , m , (-2)

To Find :–

• The value of its 2nd term (m)

Formula Applied :–

• $\boxed{\bf{\star\:\:a_n\:=\:a\:+\:(n\:-\:1)d\:\:\star}}$

• $\boxed{\bf{\star\:\:d\:=\:a_{n+1}-a_{n}\:\:\star}}$

Solution :–

We have , a = 10 , a₂ = m and a₃ = (-2) .

$\sf{\rightarrow \:\:\:\: a_3\:=\:(-2)}$

$\sf{\implies\:a_3\:=\:a\:+\:(3\:-\:1)d}$

$\sf{\implies\:(-2)\:=\:10\:+\:2d}$

$\sf{\implies\:2d\:=\:(-2)\:-\:10}$

$\sf{\implies\:2d\:=\:(-12)}$

$\sf{\implies\:d\:=\:(-\dfrac{12}{2}) }$

$\sf{\bigstar\:\:\:\boxed{\sf{d\:=\:(-6)}}}$

Now, we have a₂ = m , d = (-6) and n = 2.

$\sf{\implies\:a_2\:=\:a\:+\:(2\:-\:1)d}$

$\sf{\implies\:m\:=\:10\:+\:(1)\:\times\:(-6)}$

$\sf{\implies\:m\:=\:10\:+\:(-6)}$

$\sf{\implies\:m\:=\:10\:-\:6}$

${\sf\bigstar\:\:\:\:\:\boxed{\sf{m\:=\:4}}\:\:\:\:\:\bigstar}$

∴ The option (a.) is correct m = 4 .

Answer 2

Answer:

Step-by-step explanation: