Question

TIMED HURRY!! What is the sum of the series

Answer 1

Answer:

$\mathsf {5,490}$

Step-by-step explanation:

$\textsf {Given :}$

$\lim_{1 \to \660} \sum3n$

$\textsf {Finding the necessary :}$

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

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

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

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

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

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

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

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

$\implies \mathsf {S_n =\frac{n}{2}(a + a_n) }$

$\implies \mathsf {S_6_0 = \frac{60}{2} (3 + 180)}$

$\implies \mathsf {S_6_0 = 30 \times 183}$

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

Answer 2

$\\ \rm\Rrightarrow \sum^{60}_{n=1}3n$

It will form a arithmetic sequence as

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

• Common difference=6/3=2
• First term=a=3
• Last term=3(60)=180
• n=60-1=59

So

Summation

$\\ \rm\Rrightarrow \dfrac{n}{2}(a+\ell)$

$\\ \rm\Rrightarrow \dfrac{59}{2}(3+180)$

$\\ \rm\Rrightarrow \dfrac{59}{2}(183)$

$\\ \rm\Rrightarrow 5398.5$

Option C