Question

find common difference of an ap in which a16 - a12 =16

Answer 1

a16 - a12 = 16
a + 15d - ( a + 11d ) = 16.
a + 15d - a -11d = 16
4d = 16.
Therefore the common difference
d = 4.

Answer 2

Answer:

4

Step-by-step explanation:

Formula of nth term in A.P. = $a_n=a+(n-1)d$   --1

Where a is the first term

d is the common difference

Substitute n = 16

$a_{16}=a+(16-1)d$

$a_{16}=a+15d$

Substitute n = 12 in 1

$a_{12}=a+(12-1)d$

$a_{12}=a+11d$

Since we are given that $a_{16}-a_{12}=16$

$\Rightarrow a+15d - a-11d =16$

$\Rightarrow 15d -11d =16$

$\Rightarrow 4d =16$

$\Rightarrow d =\frac{16}{4}$

$\Rightarrow d = 4$

Hence the common difference is 4