Oblicz sume ciagu arytm

[matmabee]

a) \(6,13,20,27,... S_{13}=?\)
b) \(-91,-80,-69,-58,... S_{20}=?\)
c)\( \frac{3}{4},2,3\frac{1}{4},4\frac{1}{2},...\;\;\;\;S_{24}=?\)
d)\(-0,12,-0,45, -0,78, -1,11, ... S_{18}=?\)
e)\( 50,49,48, 47,... S_{99}=?\)
f) \(\sqrt{3}-1, 2\sqrt{3}-2, 3\sqrt{3}-3.4\sqrt{3}-4,... S_{15}=?\)

[eresh]

a) \(6,13,20,27,... S_{13}=\)?

\(a_1=6\\
r=13-6=7\\
S_{n}=\frac{2a_1+(n-1)r}{2}\cdot n\\
S_{13}=\frac{12+12\cdot 7}{2}\cdot 13\\
S_{13}=624\)

[eresh]

f) \(\sqrt{3}-1, 2\sqrt{3}-2, 3\sqrt{3}-3.4\sqrt{3}-4,... S_{15}=?\)

\(a_1=\sqrt{3}-1\\
r=2\sqrt{3}-2-\sqrt{3}+1\\
r=\sqrt{3}-1\\
S_{15}=\frac{2\sqrt{3}-2+14\cdot (\sqrt{3}-1)}{2}\cdot 15\\
S_{15}=\frac{16\sqrt{3}-16}{2}\cdot 15\\
S_{15}=120\sqrt{3}-120\)

resztę spróbuj sam