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

Let an = 89

AP = 4, 9, 14, …89

Here, a = 4, d = 14 – 9 = 5

We know that

an = a + (n – 1)d

89 = 4 + (n – 1)5

85 = (n – 1)5

17 = n – 1

18 = n

So, 89 is the 18th 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.

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