Question

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Answer 1

Sum of 100 terms of the sequence = 15050

Explanation:

Given expression which represents a sequence is,

`\sum_(r=1)^(100)(3r-1)`

So the sequence will be,

2, 5, 8, 11, 14..........

So, the given sequence is an arithmetic sequence with,

First term of the sequence 'a' = 2

Common difference 'd' = 5 - 2 = 3

Sum of 'n' terms of an arithmetic sequence is given by,

`S_n=(n)/(2)[2a+(n-1)d]`

Here, n = number of terms

a = first term

d = common difference

`S_(100)` =
`(100)/(2)[2(2)+(100-1)(3)]`

= 50[4 + 297]

= 15050

Therefore, sum of 100 terms of the sequence = 15050