# Which term of the AP 3, 8, 13, 18, ... will be 55 more than its 20th term?

In the given AP, the first term = a = 3

Common difference = d = 8 - 3 = 5

To find: place of the term which is 55 more than its 20th term.

So, we first find its 20th term.

Since, we know that

an = a + (n - 1) × d

a20 = 3 + (20 - 1) × 5

a20 = 3 + 19 × 5

a20 = 3 + 95

a20 = 98

20th term of the AP is 98.

Now, 55 more than 20th term of the AP is 55 + 98 = 153.

So, to find: place of the term 153.

So, let an = 153

Since, we know that

an = a + (n - 1) × d

153 = 3 + (n - 1) × 5

153 - 3 = 5n - 5

150 = 5n - 5

150 + 5 = 5n

5n = 155

n = 155/5 = 31

31st term of the AP is the term which is 55 more than 20th term.

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