Question

If an =5n-12,then a12-a10 is

Answer 1

Answer:

an=a+(n-1)d

5n-12=a+(n-1)d

5n-12=a+nd-d

5n-12=(a-d)+nd

comparing coefficient

then

5n=nd

d=5n/n

so

d=5

put the value of d

an=a+(n-1)d

5n-12=a+(n-1)5

5n-12=a+5n-5

remove 5n both side

-12+5=a

a=-7

By putting the value of A and D you will find the answer

hope u will understand

Answer 2

The value of $a_{12}-a_{10}=10$

Explanation:

We have,

$a_n =5n-12$

To find, the value of $a_{12}-a_{10}=?$

Put n = 1, 2, 3, 4, .......,

The first term of an AP.,

$a_{1}=5(1)-12=4-12=-7$

The second term of an AP.,

$a_{2}=5(2)-12=10-12=-2$

.....

The tenth term of an AP.,

$a_{10}=5(10)-12=50-12=38$

The twelvth term of an AP.,

$a_{12}=5(12)-12=60-12=48$

∴ $a_{12}-a_{10}$

= 48 - 38

= 10

Hence, the value of $a_{12}-a_{10}=10$