geometrik progressiya dastlabki n ta hadi yig'indisi
![Geomet rik progressiy a
dast labk i n t a hadi y ig’indisi](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_1.png)
![Maxraji bo’lgan geomet rik
progressiy aning dast labk i n t a
hadining y ig’indisi : ?????? ?????? =
?????? ?????? ( ?????? − ??????
??????
)
?????? − ??????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_2.png)
![Masala 1
geomet rik progressiy a
dast labk i y et t it a hadi y ig’indisini t oping.
?????? ??????= ?
?????? =
?????? ??????
?????? ??????
=
????????????
??????
= ??????
?????? ?????? =
?????? ∙ (?????? − ??????
??????
)
?????? − ??????
=
?????? ∙ ( − ?????????????????? )
− ??????
= ??????????????????
?????? ?????? =
?????? ?????? (?????? − ??????
??????
)
?????? − ??????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_3.png)
![Masala 2 A gar geomet rik
progressiy ada
, ga t eng bo’lsa, uning
birinchi hadini t oping. ?????? ?????? =
?????? ?????? (?????? − ??????
??????
)
?????? − ??????
?????? ?????? =
?????? ?????? (?????? − ?????? )
?????? − ??????
??????
?????? ?????? =
?????????????????? ∙
(
?????? −
??????
?????? )
?????? −
(
??????
?????? )
?????? =
?????????????????? ∙
??????
??????
????????????
????????????
= ??????????????????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_4.png)
![Masala 3 A gar geomet rik
progressiy ada
, bo’lsa, ? ?????? ?????? =
?????? ?????? (?????? − ??????
??????
)
?????? − ??????
− ???????????? =
− ?????? ∙ (?????? − ??????
??????
)
?????? − ??????
− ???????????? = ?????? − ??????
??????
??????
??????
= ???????????? ??????
??????
= ??????
??????
?????? = ??????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_5.png)
![Masala 4
?????? − ?????? = ??????
?????? ?????? =
?????? ?????? (?????? − ??????
??????
)
?????? − ??????
=
?????? ∙ (?????? − ??????
??????
)
?????? − ??????
= ???????????????????????? y ig’indisini t oping.
?????? =
?????? ??????
?????? ??????
=
????????????
??????
= ??????
??????
?????? − ??????
= ?????????????????? = ??????
?????? ?????? = ??????
??????
?????? − ??????
=
?????? ??????
?????? ??????
??????
?????? − ??????
=
????????????????????????
??????
?????? ?????? = ?????? ?????? ∙ ??????
?????? − ??????
?????? ?????? = ?????? ?????? ∙ ??????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_6.png)
![Masala 5 A gar geomet rik
progressiy ada
, bo’lsa, ? ?????? ?????? = ?????? ?????? ??????
?????? ?????? = ?????? ?????? ??????
??????
?????? ??????
?????? ??????
=
??????
??????
??????
?????? =
??????
??????
?????? ?????? =
?????? ??????
??????
=
????????????
??????
??????
= ??????
?????? ?????? =
?????? ?????? (?????? − ??????
??????
)
?????? − ??????
= ????????????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_7.png)
![](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_8.png)
![????????????
??????
????????????
??????
????????????
??????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_9.png)
![A gar geomet rik progressiy ada
bo’lsa, ??????
??????
??????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_10.png)
![geomet rik progressiy ada dast labk i
y et t it a hadi y ig’indisini t oping.????????????????????????
????????????????????????
????????????????????????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_11.png)
![????????????
????????????
????????????
????????????
????????????
????????????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_12.png)
![A gar geomet rik progressiy ada
, , ??????
??????
??????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_13.png)
![y ig’indini t oping. ????????????
8
????????????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_14.png)
![geomet rik progressiy ada dast labk i
y et t it a hadi y ig’indisini t oping.??????????????????
??????
??????
??????????????????
??????????????????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_15.png)
![??????????????????
????????????
−
??????????????????
????????????
????????????
??????????????????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_16.png)
![A gar geomet rik progressiy ada
, , ??????
??????
??????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_17.png)
![, bo’lsa, ??????????????????
??????????????????
??????????????????](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_18.png)
![Qolgan misollarni must aqil
y echishga harak at qiling!](/data/documents/802781f5-dbd2-4ae8-915e-b80a45869019/page_19.png)
Geomet rik progressiy a dast labk i n t a hadi y ig’indisi
Maxraji bo’lgan geomet rik progressiy aning dast labk i n t a hadining y ig’indisi : ?????? ?????? = ?????? ?????? ( ?????? − ?????? ?????? ) ?????? − ??????
Masala 1 geomet rik progressiy a dast labk i y et t it a hadi y ig’indisini t oping. ?????? ??????= ? ?????? = ?????? ?????? ?????? ?????? = ???????????? ?????? = ?????? ?????? ?????? = ?????? ∙ (?????? − ?????? ?????? ) ?????? − ?????? = ?????? ∙ ( − ?????????????????? ) − ?????? = ?????????????????? ?????? ?????? = ?????? ?????? (?????? − ?????? ?????? ) ?????? − ??????
Masala 2 A gar geomet rik progressiy ada , ga t eng bo’lsa, uning birinchi hadini t oping. ?????? ?????? = ?????? ?????? (?????? − ?????? ?????? ) ?????? − ?????? ?????? ?????? = ?????? ?????? (?????? − ?????? ) ?????? − ?????? ?????? ?????? ?????? = ?????????????????? ∙ ( ?????? − ?????? ?????? ) ?????? − ( ?????? ?????? ) ?????? = ?????????????????? ∙ ?????? ?????? ???????????? ???????????? = ??????????????????
Masala 3 A gar geomet rik progressiy ada , bo’lsa, ? ?????? ?????? = ?????? ?????? (?????? − ?????? ?????? ) ?????? − ?????? − ???????????? = − ?????? ∙ (?????? − ?????? ?????? ) ?????? − ?????? − ???????????? = ?????? − ?????? ?????? ?????? ?????? = ???????????? ?????? ?????? = ?????? ?????? ?????? = ??????