Which term of the A.P. 4, 9, 14, ... is 89? Also, find the sum 4 + 9 + 14 + + 89.

Let a_n = 89

AP = 4, 9, 14, …89

Here, a = 4, d = 14 – 9 = 5

We know that

a_n = a + (n – 1)d

⇒ 89 = 4 + (n – 1)5

⇒ 85 = (n – 1)5

⇒ 17 = n – 1

⇒ 18 = n

So, 89 is the 18^th term of the given AP

Now, we find the sum of 4 + 9 + 14 + … + 89

We know that,

⇒ S₁₈ = 9[8 + 17 × 5]

⇒ S₁₈ = 9[8 + 85]

⇒ S₁₈ = 9 × 93

⇒ S₁₈ = 837

Hence, the sum of the given AP is 837.