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Find the sum of the first 36 terms of the following series, to the nearest integer.
7, 12, 17,...
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S₃₆ = 3402

Step-by-step explanation:

there is a common difference between term in the sequence , that is

12 - 7 = 17 - 12 = 5

this indicates the sequence is arithmetic with sum to n terms

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 7 and d = 5 , then

S₃₆ = [tex]\frac{36}{2}[/tex] [ (2 × 7) + (35 × 5) ]

= 18( 14 + 175)

= 18 × 189

= 3402
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