1

kwJym{I-a-§Ä

1 sk.ao. 2 sk.ao. 3 sk.ao. 4 sk.ao.

Nn{X-¯nse ka-N-Xp-c-§Ä t\m¡q, Ah-bpsS Npä-fhv F{X-bmWv?
]c-¸-fthm?
hi-§-fpsS \ofw

1 sk.ao., 2 sk.ao., 3 sk.ao., 4 sk.ao., ...
F¶n-§s\ XpS-cp-t¼mÄ, Npä-fhv

4 sk.ao., 8 sk.ao., 12 sk.ao., 16 sk.ao., ...
F¶p XpS-cp¶p; ]c-¸-fhv

1 N.sk.ao., 4 N.sk.ao., 9 N.sk.ao., 16 N.sk.ao., ...
F¶pw.
kwJy-IÄ am{X-ambn ]d-ªmtem?
hi-§-fpsS \ofw

1, 2, 3, 4, ...
F¶n-§s\ F®Âkw-Jy-IÄ {Ia-ambn Fgp-Xp-¶-Xp-Xs¶. Npä-fhv

4, 8, 12, 16, ...
F¶n-§s\ \mensâ KpWn-X-§-fpsS {Iaw; ]c-¸-fhv,

1, 4, 9, 16, ...
F¶ ]qÀW-hÀK-§-fpsS {Iaw.



















kam-´ct{iWn-IÄ

""Htc kwJy XpSsc Iq«pI'' F¶-Xns\ ""Htc kwJy XpSsc Iq«p-
Itbm XpSsc Ipd-bv¡p-Itbm sN¿pI'' F¶p amämw. AsÃ-¦n ""2
Ipd-bv¡pI F¶mÂ, −2 Iq«pI'' F¶v KWn-X-`m-j-bn-eqsS \ymbo-I-cn-
¡mw.
kam-´-c-t{i-Wn-Isf asämcp Xc-¯nepw hnh-cn-¡mw. C¯-c-samcp
t{iWn-bnÂ, GXp Øm\-s¯bpw ]Z-¯nÂ\n¶v sXm«p ap¶n-epÅ
]Z-¯n-se-¯m³ Htc kwJy-bm-WtÃm Iqt«-­-Xv. At¸mÄ GXp ]Z-
¯nÂ\n¶pw sXm«p-]p-d-Inse ]Zw Ipd-¨m In«p-¶Xv Cu kwJy-X-
s¶-bm-Wv.

kGwXJpy]-XZ-s-¯¶ n-IÂn-«\p¶n¶tp{wisWXnm-b«pm-]Wp-dv -Iknasme-´]-c-tZ{wiI-Wpdn.-¨m Htc

Hcp ]Z-¯nÂ\n¶v sXm«p-]p-d-Inse ]Zw Ipd¨p In«p¶ Cu Ønc-hy-
Xym-ks¯ kam-´-c-t{i-Wn-bpsS s]mXph- yX- ymkw (common difference)
F¶mWv ]d-bp-¶-Xv.
]e-t¸mgpw kam-´-c-t{i-Wn-bmtWm F¶p ]cn-tim-[n-¡p-¶-Xv,
]Z-hy-Xymkw Ønc-amtWm F¶p t\m¡n-bm-Wv. DZm-l-c-W-am-bn,
3 sâ KpWn-X-§Ä t\m¡q:

3, 6, 9, ...

3 sâ ASp-¯-Sp¯ c­p KpWnX§Ä X½n-epÅ hyXymkw 3 Xs¶-
bm-W-tÃm. At¸mÄ CXv s]mXp-hy-Xymkw 3 Bb Hcp kam-´-c-t{i-
Wn-bm-Wv.

C\n Cu KpWn-X-§-tfm-tcm-¶n-t\mSpw 1 Iq«n-bmtem?

4, 7, 10, ...

F¶ t{iWn In«pw.

CXpw 3 s]mXp-hy-Xym-k-amb kam-´-ct{iWn X-s¶.

C\n 3 sâ IrXn-IfpsS t{iWn t\m¡q:

3, 9, 27, ...

9 − 3 = 6 Dw 27 − 9 = 18 Dw; AXm-b-Xv, ASp-¯-Sp¯ ]Z-§Ä X½n-ep-Å
hyXymkw Htc kwJy-bÃ.

CsXmcp kam-´-c-t{i-Wn-bp-aÃ.

C\n CXp-hsc I­ t{iWn-I-sfÃmw H¶p-IqSn t\m¡n, Ah-bnse
kam-´-c-t{i-Wn-IÄ I­p-]n-Sn¡p-I.

17



















kam-´ct{iWn-IÄ

]Zhpw am{Xw Iq«n-bm \Sp-hnse ]Z-¯nsâ c­p aS-§m-It­? (Hcp
kwJybpw AXnsâ c­p aS§pw tNÀ¶-Xm-WtÃm aq¶p aS-§v)
CXv asäm-cp-X-c-¯n ]dbmw
GXp kam-´-c-t{i-Wn-bn-sebpw ASp-¯-Sp¯ aq¶p ]Z-§-sf-Sp-¯mÂ
BZy]Z¯- ns- âbpw Ahkm\]Z- ¯- ns- âbpw XpIb- psS ]IpX- nb- mWv \Sp-
hnse ]Zw.
ASp-¯-Sp¯ A©p ]Z-§-fn BZy-s¯bpw Ah-km-\-s¯bpw Iq«n-
bmtem? c­m-a-s¯bpw \mem-a-s¯bpw ]Z-§-fm-bmtem?
CXp-t]mse ASp-¯-Sp¯ Ggp ]Z-§-fnÂ, \S-p¡p-\n¶v Ccp-hi¯pw
Htc AI-e-¯n-epÅ ]Z-§-fpsS tPmSn-IÄ Iq«n-t\m-¡q.
CXp-hsc ]Z-§-fpsS F®w Hä-kwJy Bbn-«mWv FSp-¯-Xv. Cc-«-kwJy
Bbmtem?
GsX¦- ne- ps- amcp kam´- c- t- {iW- nb- nse XpSÀ¨b- mb \mep ]Z§- s- fSp¯p
t\m¡mw. DZm-l-c-W-am-bn, 5, 8, 11, 14 CXn \Sp¡v F¶p ]d-bm³ Hcp
]Zw CÃm-¯-Xn-\mÂ, BZyw I­ s]mXp-XXzw t]mse H¶pw ]d-bm³
Ign-bn-Ã. c­m-aXp sNbvX-Xp-t]m-se, BZy-s¯bpw Ah-km-\-s¯bpw
]Z-§-fpsS tPmSn-bpw, c­m-a-s¯bpw aq¶m-a-s¯bpw ]Z-§-fpsS
tPmSnbpw Iq«n t\m¡mw: 5 + 14 = 8 + 11
Bdp ]Z§-fm-bmtem? GsXms¡ tPmSn-I-fpsS XpI-I-fmWv Xpey-am-Ip-
¶Xv?
GXp kam-´-c-t{i-Wn-sbbpw s]mXpsh an + b F¶ cq]-¯n Fgp-
Xm-a-tÃm. CXnse \me-ma-s¯bpw A©m-a-s¯bpw ]Z-§Ä Fs´m-
s¡-bmWv? Ah-bpsS XpItbm?

(4a + b) + (5a + b) = 9a + 2b

CtX XpI In«p¶ aäp c­p ]Z-§Ä ]d-bmtam?
9 s\ 2 + 7 F¶pw Fgp-Xm-a-tÃm. At¸mÄ c­m-a-s¯bpw Ggm-a-s¯bpw
]Z-§-fpsS XpI F´mWv?
CtX XpI In«p¶ asämcp tPmSn?
Hcp kam-´-c-t{i-Wn-bnse A©m-a-s¯bpw ]¯m-a-s¯bpw ]Z-§-fpsS
XpI In«p¶ aäp c­p Øm\-§Ä ]d-bmtam?
CXnÂ\n-s¶Ãmw In«p¶ s]mXp-XXzw F´mWv?

Hcp kam-´-c-t{i-Wn-bn-se GsX-¦nepw c­p tPmSn Øm\-§-
fpsS XpI Xpey-am-sW-¦nÂ, B Øm\-§-fnse ]Z-§-fpsS
XpIbpw Xpey-am-bn-cn-¡pw.
C\n Cu IW¡p t\m¡q: Hcp kam-´-c-t{i-Wn-bpsS BZys¯ ]Zw
5 Dw BZys¯ Bdp ]Z-§-fpsS XpI 105 Dw BWv. t{iWn I­p-]n-Sn-
¡mtam?

27