Question

TIMED HURRY!! What is the sum of the series

possible answers
1,830
2,010
5,400
5,490

Answer 1

`\mathsf {5,490}`

Explanation:

`\textsf {Given :}`

`\lim_(1 \to \660) \sum3n`

`\textsf {Finding the necessary :}`

`\textsf {1. first term (a)}`

`\implies \mathsf {a = 3(1) = 3}`

`\textsf {2. final term}`
`\mathsf {(a_n)}`

`\implies \mathsf {a_n = 3(60) = 180}`

`\textsf {3. common difference (d)}`

`\implies \mathsf {a_2 = 3(2) = 6}`

`\implies \mathsf {d = a_2 - a_1 = 6 - 3 = 3}`

`\textsf {Finding the sum of the series :}`

`\implies \mathsf {S_n =(n)/(2)(a + a_n) }`

`\implies \mathsf {S_6_0 = (60)/(2) (3 + 180)}`

`\implies \mathsf {S_6_0 = 30 * 183}`

`\implies \mathsf {S_6_0 = 5,490}`

Answer 2

`\\ \rm\Rrightarrow \sum^(60)_(n=1)3n`

It will form a arithmetic sequence as

`\\ \rm\Rrightarrow 3(1)+3(2)+3(3)\dots 3(60)`

• First term=a=3
• Last term=3(60)=180
• n=60

So

Summation

`\\ \rm\Rrightarrow (n)/(2)(a+\ell)`

`\\ \rm\Rrightarrow (60)/(2)(3+180)`

`\\ \rm\Rrightarrow 30(183)`

`\\ \rm\Rrightarrow 5490`

Option D