(i) 7, 13, 19, …, 205

(ii)

Solutions:

(i) Given here, 7, 13, 19, …, 205 is the A.P

Therefore

The first term, a = 7

The common difference, d = a₂ − a₁ = 13 − 7 = 6

Let us assume that there are n terms in this A.P.

a_n = 205

As we all know, for an A.P.,

a_n = a + (n − 1) d

Therefore, 205 = 7 + (n − 1) 6

198 = (n − 1) 6

33 = (n − 1)

n = 34

Therefore, the above given series has 34 terms in it.

(ii) Given here, 18, 15 ,13… -47 is the A.P.

The first term, a = 18

The common difference, d = a₂-a₁ =

d = (31-36)/2 = -5/2

Let us assume that there are n terms in this A.P.

a_n = 205

As we all know, for an A.P.,

a_n = a+(n−1)d

-47 = 18+(n-1)(-5/2)

-47-18 = (n-1)(-5/2)

-65 = (n-1)(-5/2)

(n-1) = -130/-5

(n-1) = 26

n = 27

Therefore, the above given A.P. has 27 terms in it.