Odpowiedź:
[tex]a_4 = a_1 + 3 r = 21\\a_{12} = a_1 + 11 r = 53[/tex]
------------ odejmujemy stronami
( [tex]a_1 + 11 r) - ( a_1 + 3 r) = 53 - 21 = 32[/tex]
8 r = 32 / : 8
r = 4
====
[tex]a_1 + 3*4 = 21[/tex]
[tex]a_1 = 21 - 12 = 9[/tex]
==============
[tex]a_{25} = a_1 + 24 r =[/tex] 9 + 24*4 = 9 + 96 = 105
S[tex]_{25} = \frac{a_1 + a_{25}}{2} *25 =[/tex] [tex]\frac{9 + 105}{2}* 25 = 57*25 = 1 425[/tex]
Szczegółowe wyjaśnienie:
Korzystamy z wzorów:
[tex]a_n = a_1 + ( n - 1)*r\\S_n = \frac{a_1 + a_n}{2}* n[/tex]
