Question

I NEED HELP QUICKLY!! Find the sum of the first 42 terms of the sequences (12, 16, 20, ....)

A) 3,717
B) 3,948
C) 1,134
D) 4,032

Answer 1

B

Explanation:

Note the common difference between consecutive terms of the sequence.

d = 16 - 12 = 20 - 16 = 4

This indicates the sequence is arithmetic with sum to n terms

`S_(n)` =
`(n)/(2)` [2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 12 and d = 4, thus

`S_(42)` =
`(42)/(2)` [ (2 × 12) + (41 × 4) ]

= 21( 24 + 164) = 21 × 188 = 3948 → B