Question

Show that a1,a2,.......an,.. form an AP where an is defined as below( 1)an=3+4n (2)an=9-5n

Answer 1

Here is your Answer

Answer 2

●First of all find the first term, a.

So, for (1)

answer➡️ a 1= 3 + 4(1) = 7

●Now find the 2nd term:-

➡️a 2 = 3 + 4(2) = 11

So, common difference (d) = 11- 7 =4

Third term :-

a3 = 3 + 4(3) = 15

Again d = 15 - 11 = 4

Since the common difference is same hence it is an Arithmetic Progression.

●Now question no. (2)

a1= 9 - 5(1) = 4

a2 = 9 - 5(2) = -1

d = -1 - 4 = -5

again a3 = 9 - 5(3) = -6

again d = -6 + 1 = -5

So we can see that d is constant, so it is an Arithmetic Progression.