a) 3,717

b) 3,948

c) 1,134

d) 4,032

17,661

Step-by-step explanation:

-10, 2, 14, 26

T1 = a = -10

T2 = 2

T3 = 14

T4 = 26

Lets find the common difference

T2 - T1 = T3 - T2

2 - (-10) = 12 = 14 - 2 = 12

common difference d = 12

therefore, this is an arithmetic progression

Sum of first 42 terms

S42 = n/2 [2a + (n - 1) * d]

where n = 42

slot in the values

S42 = 42/2 [2*(-10) + (42 -1)* 12]

S42 = 21[ -20 + (41*12)]

S42 = 21 ( -20 + 861)

S42 = 21( 841)

S42 = 17,661

B

Step-by-step 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

= [2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 12 and d = 4, thus

= [ (2 × 12) + (41 × 4) ]

= 21( 24 + 164) = 21 × 188 = 3948 → B

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