Question

Find the common difference of the A.P whose first term is 12 and fifth term is 0.

Answer 1

The common difference of an A.P is -3.

Step-by-step explanation:

Given : An A.P whose first term is 12 and fifth term is 0.

To find : The common difference of an A.P ?

Solution :

The first term of an A.P is a=12

The fifth term of an A.P is a_5=a+4da5=a+4d

We have given, a_5=0a5=0

Substitute the value,

0=12+4d0=12+4d

4d=-124d=−12

d=-\frac{12}{4}d=−412

d=-3d=−3

The common difference of an A.P is -3.

#Learn more

The comman difference of the A.P. is d = 5 & first term a = 10 then find the next two terms of a.p

$hence \: solved$

Answer 2

ɢɪᴠᴇɴ:

• First term of an AP is 12.
• Fifth term of an AP is 0.

ᴛᴏ ғɪɴᴅ:

• The common difference of the AP.

ᴀɴsᴡᴇʀ:

Arithmetic Progression:

• When a common number is added to each term to form a new term , them it is called AP .

Now we know a formula to find the n th term of an AP as

$\large{\underline{\boxed{\red{\bf{\dag T_n = a+(n-1)d}}}}}$

Where ,

• a is first term.
• d is common difference.
• n is the number of terms.

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

$\sf{\implies T_5 = 12 + (5-1)d}$

$\sf{\implies 0 = 12 + 4d}$

$\sf{\implies 4d = -12 }$

$\sf{\implies d = \dfrac{-12}{4}}$

$\bf{\implies \red{\dag} \purple{d= -3}\red{\dag}}$

Hence the common difference is (-3)