Question

( PICTURE) SIGMA NOTATION AND THE NTH TERM
HELP ASAPP !!!!

Answer 1

`\sum _(k=1)^4\:\:\left(3k+3\right)`

option-d

Explanation:

we are given series as

`6+9+12+15`

so, first term is 6

`a_1=6`

now, we can find common difference

`d=9-6`

`d=3`

now, we can find kth term

`a_k=a_1+(k-1)d`

we can plug values

`a_k=6+(k-1)* 3`

`a_k=6+3k-3`

`a_k=3k+3`

Since, there are four terms

so, k varies from 1 to 4

so, we get series as

`\sum _(k=1)^4\:\:\left(3k+3\right)`