Question

Find the number of terms of A.P 100,105,110,115,.........500.​

Answer 1

Answer:

$number \: of \: terms \: = a_{n} = a + (n-1)d$

$where \: a = first \: term = 100 \\ n = number \: of \: terms \\ d = common \: difference \\ a _{n} = last \: term = 500$

$500= 100 + (n - 1)5 \\ 500 = 100 + 5n - 5 \\ 500= 95 + 5n \\ 5n = 500 - 95 \\ 5n = 405 \\ n = \frac{405}{5} = 81$

The number of terms in the given A.P are 81.

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