Question

find all arithmetic progression with a difference 10 formed of more than two primes.​

Answer 1

Answer:

Step-by-step explanation:

d = 10

let n =3 first A.P

then (n + a d) = 2nd A.P

the value of a must not be multiple of 3 so we can say that a= 0,1, 2 is possible.

So A1  = (3 + o)=3

    A2 = (3 + 10)=13

   A3 = (3 +20) = 23

so these three number is all arthimetic progression with a difference 10 formed of more than two primes.

Answer 2

Given :  arithmetic progression with a difference 10 formed of more than two primes.​

To Find : all  such cases

Solution:

3 , 13 , 23  is arithmetic progression with a difference 10 formed of more than two primes.​

for numbers greater than 3  prime numbers are of form

6q - 1 ,  6q + 1

Let say    6q - 1   is 1st prime number then next will be

6q - 1  + 10  

= 6q + 9

= 3(q + 3) hence  not a prime number

Let say  6q + 1   is 1st prime number then next two  will be

6q + 1 + 10  , 6q + 1 + 20

= 6q + 11  ,  6q  + 21  

= 6*(q + 2) - 1  ,   3(2q + 7)

= 6k - 1 ,       while           3(2q + 7)  not a prime number

Hence more than two primes are not possible

so only combination is  3  , 13 , 23

Learn More:

The 4 term of an ap is 10

brainly.in/question/8425614

Question from some special series and AP

brainly.in/question/12764784