Question

cunoscând suma Sn a primilor n termeni ai unei progresii aritmetice an, sa se găsească:

Answer 1

Explicație pas cu pas:

a)

$S_{1} = a_{1}$

$a_{1} = \dfrac{1^{2}}{4} - 1 = \dfrac{1}{4} - 1 = - \dfrac{3}{4}$

$S_{2} = a_{1} + a_{2}$

$a_{2} = \bigg( \dfrac{2^{2}}{4} - 2\bigg) - \bigg(- \dfrac{3}{4}\bigg) = - 1 + \dfrac{3}{4} = - \dfrac{1}{4}$

$r = a_{2} - a_{1} = - \dfrac{1}{4} + \dfrac{3}{4} = \bf \dfrac{1}{2}$

$a_{3} = a_{1} + 2r = - \dfrac{3}{4} + 2 \cdot \dfrac{1}{2} = - \dfrac{3}{4} + 1 = \dfrac{1}{4}$

$a_{4} = a_{1} + 3r = - \dfrac{3}{4} + 3 \cdot \dfrac{1}{2} = - \dfrac{3}{4} + \dfrac{3}{2} = \dfrac{3}{4}$

$a_{5} = a_{1} + 4r = - \dfrac{3}{4} + 4 \cdot \dfrac{1}{2} = - \dfrac{3}{4} + 2 = \dfrac{5}{4}$

b)

$S_{1} = a_{1}$

$a_{1} = 2 \cdot 1^{2} + 3 \cdot 1 = 2 + 3 = \bf 5$

$S_{2} = a_{1} + a_{2}$

$a_{2} = (2 \cdot 2^{2} + 3 \cdot 2) - 5 = 8 + 6 - 5 = 9$

$r = a_{2} - a_{1} = 9 - 5 = \bf 4$