Answer:
245 and 55050
Step-by-step explanation:
The sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
In the first progression a₁ = 2 and d = 7 - 2 = 5, thus
[tex]S_{10}[/tex] = [tex]\frac{10}{2}[/tex] [ (2 × 2) + (9 × 5) ] = 5 × ( 4 + 45 ) = 5 × 49 = 245
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In the second progression a₁ = 6 and d = 17 - 6 = 11, thus
[tex]S_{100}[/tex] = [tex]\frac{100}{2}[/tex] [ (2 × 6) + (99 × 11) ]
= 50(12 + 1089) = 50 × 1101 = 55050
