Question

Gasiti S30 daca ıntr-o progresie aritmetica avem: a8 + a13 + a18 + a23 = 30.

Answer 1

[tex]\it a_8 + a_{13} + a_{18} + a_{23} = 30 \Leftrightarrow a_1+7r+a_1+12r+a_1+17r+ \\ \\ a_1+22r = 30 \Leftrightarrow 4a_1 + 58r=30|_{:2} \Leftrightarrow 2a_1+29r = 15 \ \ (1) [/tex]

$\it S_{30} =\dfrac{30(a_1+a_{30})}{2}= 15(a_1+a_1+29r) = 15(2a_1+29r)\ \ (2)$

$\it (1), (2) \Rightarrow S_{30} =15\cdot 15 =225 .$

Answer 2

a8+a13+a18+a23=30
=>r=5
=>Sn=a1+a2+a3+....an
=>S30=a8+a13+a18+a23
=>S30=a8+a23=a13+a18
a8+a23=a13+a18=a1+a30
=2(a1+a30)=30
=>a1+a30=a30
=>S30=30(a1+a30)/2