If a_n denotes the n^th term of the A.P. 3, 8, 13, 18, ..., then the value of a₃₀ – a₂₀ is __________.

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Solution

The given A.P. is: 3, 8, 13, 18, ...

First term (a) = 3
Common difference (d) = 8 – 3 = 5

Now,
$a_{n} = a + (n - 1) d a_{30} = a + (30 - 1) d = a + 29 d a_{20} = a + (20 - 1) d = a + 19 d ∴ a_{30} - a_{20} = (a + 29 d) - (a + 19 d) = 29 d - 19 d = 10 d = 10 \times 5 (∵ d = 5) = 50$

Hence, the value of a₃₀ – a₂₀ is 50.

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