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What is the sum of the first 19 terms of an arithmetic series with a rate of increase of 7 and a7 = 46?

A. 1,197
B. 1,273
C. 1,373
D. 1,423
E. 1,327

Respuesta :

meerkat18
Calculate for the first term of the series
                                   an = (a1) x (n - 1) x d
Using the value of a7 = 46 and the rate of increase
                                    46 = (a1) x (7 -1) x 7
The value of a1 is 4.
Solving for the sum of 19 terms,
                                Sn = (n/2) x (2a1 + (n - 1) x d)
Substituting, 
                                Sn = (19/2) x ((2)(4) + 18 x 7)
The sum of the first 19 terms is 1,273. Therefore, the answer is letter B.

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