Show that the progression 13, 20, 27, 34, …….. is an A.P. Write down its :

(i) first term

(ii) common difference

(iii) 20th term.

Since, 20 - 13 = 7, 27 - 20 = 7, and 34 - 27 = 7.

Hence, the series is an A.P. with common difference = 7.

We know that,

n^th term of an A.P. is given by,

⇒ a_n = a + (n - 1)d, where a is the first term.

⇒ a₂₀ = 13 + (20 - 1)7

= 13 + (19) × 7

= 13 + 133

= 146.

Hence, a = 13, d = 7 and a₂₀ = 146.