Question

check weather the following sequences are in AP. 1)9,13,17,21,25...............…​

Answer 1

Hey Mate!

Here is Your Answer:

Yes, it is in sequesnce! HEre is an explantion.

Step-by-step explanation:

9, 13, 17, 21, 25

This is a pattern. Each number ha a gap of 4 numbers.

- Between 9 and 13, there is a gap of 4 numbers/units. (as 13 - 9 = 4)

-Between13 and 17, there is a gap of 4 numbers/units. (as 17 - 14 = 4)

-Between 17 and 21, there is a gap of 4 numbers/units. (as 21 - 17 = 4)

-Between 21 and 25, there is a gap of 4 numbers/units. (as 25 - 21 = 4).

And so, this pattern is in sequesnce.

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Answer 2

An arithmetic sequence (or arithmetic progression) is a sequence (finite or infinite list) of real numbers for which each term is the previous term plus a constant (called the common difference). For example, starting with 1 and using a common difference of 4 we get the finite arithmetic sequence: 9, 13, 17, 21; and also the infinite sequence

9, 13, 17, 21, 25, 29, . . ., 4n+1, . . .

In general, the terms of an arithmetic sequence with the first term a0 and common difference d, have the form an = dn+a0 (n=0,1,2,...). If a0 and d are relatively prime positive integers, then the corresponding infinite sequence contains infinitely many primes (see Dirichlet's theorem on primes in arithmetic progressions).

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