How many terms are there in the following Arithmetic Progressions?

(i) (ii) 7, 13, 19, …, 205.

(i) Here, first term, a = -1

Last term, l =

We know that common difference, d = a₁ – a.

∴ d = – (-1) = + 1 = =

We know that Number of terms, n = () + 1.

⇒ n = + 1

= + 1

= + 1

= (13 × 2) + 1

= 26 + 1

= 27

∴ There are 27 terms in the given A.P.

(ii) Here, first term, a = 7

Last term, l = 205

We know that common difference, d = a₁ – a.

∴ d = 13 - 7 = 6

We know that Number of terms, n = () + 1.

⇒ n = + 1

= + 1

= 33 + 1

= 34

∴ There are 34 terms in the given A.P.