183
O‘ZINGIZNI TEKSHIRIB KO‘RING!
1.
Arifmetik
progressiyada
a
1
=
2,
d
= -
3.
a
10
ni
va dastlabki
o‘nta hadning yig‘indisini toping.
2.
Geometrik progressiyada
b
1
=
4,
q
=
1
2
.
b
6
ni va dastlabki oltita
hadning yig‘indisini toping.
3.
1
1
3
1
9
,
,
,
... ketma-ketlik
cheksiz kamayuvchi geometrik
progressiya ekanligini isbotlang va uning hadlari yig‘indisini
toping.
478.
x
ning qanday qiymatlarida:
1) 3
x
,
x
+
2
2
, 2
x
-
1;
2) 3
x
2
, 2, 11
x
sonlar arifmetik progressiyaning ketma-ket hadlari bo‘ladi?
479.
Quyidagi sonlar arifmetik progressiyaning ketma-ket
uchta hadi
bo‘lishini ko‘rsating:
1) sin(
a + b
), sin
a
cos
b
, sin(
a - b
);
2) cos(
a + b
), cos
a
cos
b
, cos(
a - b
);
3) cos2
a
, cos
2
a
, 1;
4) sin5
a
, sin3
a
cos2
a
, sin
a
.
480.
Yig‘indi 252 ga teng bo‘lishi uchun 5 dan boshlab nechta ketma-
ket toq natural sonni qo‘shish kerak?
481.
Agar arifmetik progressiyada:
1)
a
1
=
40,
n
=
20,
S
20
= -
40;
2)
a
1
=
1
3
,
n
=
16,
S
16
=
3
2
10
-
bo‘lsa,
a
n
va
d
ni toping.
482.
Geometrik progressiyada:
1) agar
b
1
=
4 va
q
= -
1 bo‘lsa,
b
9
ni hisoblang;
2) agar
b
1
=
1 va
q
=
3 bo‘lsa,
b
7
ni hisoblang.
483.
Agar geometrik progressiyada:
1)
b
2
=
1
2
,
b
7
=
16;
2)
b
3
= -
3,
b
6
= -
81;
3)
b
2
=
4,
b
4
=
1;
4)
b
4
= -
1
5
,
b
6
= -
1
125
bo‘lsa, uning beshinchi hadini toping.
184
484.
4 va 9 sonlari orasiga bitta musbat sonni shunday qo‘yingki, nati-
jada geometrik progressiyaning ketma-ket uchta hadi hosil bo‘lsin.
485.
Agar
ketma-ketlik
n
- hadining:
1)
b
n
=
5
n
+
1
;
2)
b
n
=
(
-
4)
n
+
2
;
3)
n
n
b
=
10
7
;
4)
n
n
b
+
= -
3
50
3
formulasi bilan berilgan bo‘lsa, u cheksiz kamayuvchi geometrik
progressiya bo‘la oladimi?
486.
Agar geometrik progressiyada:
1)
b
2
= -
81,
S
2
=
162;
2)
b
2
=
33,
S
2
=
67;
3)
b
1
+
b
3
=
130,
b
1
-
b
3
=
120;
4)
b
2
+
b
4
=
68,
b
2
-
b
4
=
60
bo‘lsa, u cheksiz kamayuvchi ekanligini ko‘rsating.
487.
Dam oluvchi shifokor tavsiyasiga amal qilib, birinchi kuni Quyosh
nurida 5 minut toblandi, keyingi har bir kunda esa toblanishni
5 minutdan oshirib bordi. Agar u toblanishni chorshanba kunidan
boshlagan bo‘lsa, haftaning qaysi kuni uning Quyoshda toblani-
shi 40 minutga teng bo‘ladi?
488.
Agar
arifmetik progressiyada
a
1
+
a
2
+
a
3
=
15 va
a
1
×
a
2
×
a
3
=
80
bo‘lsa, uning birinchi hadi va ayirmasini toping.
489.
Agar arifmetik progressiyada
a
1
+
a
2
+
a
3
=
0 va
a
a
a
1
2
2
2
3
2
50
+
+
=
bo‘lsa, uning birinchi hadi va ayirmasini toping.
490.
Soat 1 da soat 1 marta, 2 da 2 marta, ..., 12 da 12 marta bong uradi.
Soat mili navbatdagi har soatning yarmini ko‘rsatganda esa bir
marta bong uradi. Bu soat bir sutkada necha marta bong uradi?
VI bobga doir sinov (test) mashqlari
1.
Arifmetik progressiyada
a
1
= 3,
d
= –2.
S
101
ni toping.
A) –9797; B) –9798; C) –7979; D) –2009; E) –9697.
2.
Arifmetik progressiyada
d
= 4,
S
50
= 5000 bo‘lsa,
a
1
ni toping.
A) –2; B) 2; C) 100; D) 1250; E) 5.
3.
Arifmetik progressiyada
a
1
= 1,
a
101
= 301 bo‘lsa,
d
ni toping.
A) 4; B) 2; C) 3; D) 3,5; E) 5.
4.
Arifmetik progressiyada
a
2
+
a
9
= 20 bo‘lsa,
S
10
ni toping.
A) 90; B) 110; C) 200; D) 100; E) aniqlab bo‘lmaydi.
185
5.
8 ga bo‘lganda 7 qoldiq beradigan ketma-ketlikning 5- hadini belgilang.
A) 74; B) 55; C) 39; D) 63; E) 47.
6.
701 soni 1, 8, 15, 22, ... progressiyaning nechanchi nomerli hadi?
A) 101; B) 100; C) 102; D) 99; E) bu progressiyaning hadi emas.
7.
1002, 999, 996, ... progressiyaning
nechanchi nomerli hadidan
boshlab, uning hadlari manfiy sonlar bo‘ladi?
A) 335; B) 336; C) 337; D) 334; E) 330.
8.
Arifmetik progressiyada
a
2
+
a
6
= 44,
a
5
–
a
1
= 20 bo‘lsa,
a
100
ni toping.
A) 507; B) 495; C) 502; D) 595; E) 520.
9.
Arifmetik progressiyada
a
1
= 7,
d
= 5,
S
n
= 25450 bo‘lsa,
n
ni
toping.
A) 99; B) 101; C) 10; D) 100; E) 590.
10.
Arifmetik progressiya
a
12
+
a
15
= 20 bo‘lsa,
S
26
ni toping.
A) 540; B) 270; C) 520; D) 130; E) 260.
11.
1 va 11 sonlari orasida 99 ta shunday sonni joylashtiringki, ular
bu sonlar bilan birgalikda arifmetik progressiya tashkil qilsin.
Shu progressiya uchun
S
50
ni toping.
A)
1
2
172 ; B) 495; C) 300; D) 178; E) 345.
12.
Arifmetik progressiyada
a
1
= –20,7,
d
= 1,8 bo‘lsa, qaysi nomerli
haddan boshlab progressiyaning barcha hadlari musbat bo‘ladi?
A) 18; B) 13; C) 12; D) 15; E) 17.
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