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A collection of exercises and problems related to arithmetic progressions (ap) in mathematics. It covers various aspects of ap, including finding the common difference, determining the nth term, calculating the sum of terms, and solving problems involving specific conditions. A comprehensive set of examples and solutions, making it a valuable resource for students studying ap.
Typology: Study notes
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the P.
the ,
OF
an a+ d (n-1)
tenmn
AP
#n tenmof A.P -
difFeHence
O ption la)-Ais false
Qtad ,at3d
5,1, is 4 -3,- Reason
PHEVÍous teum
Obtaine adding.xed no. to the
ceSequenin which each
? AsseHtion Common
+AR A
*LAim in(00/100 Mathematics
) The
12,..1. a (^) a t (^) ( 40d 32 *d 6 - at(n-i)d r+ aad -a- 18d = 32
numben Qad- |8d 2 d
6, 9, |2 , .. 111 i .. *an^ =^ 1J3+ of (^) tenmg a +ln-)d = W n -)3 I| in (^) the (unknon tm
n = 8 65
n 65| "4)The 7h tenm (^) fnom AP. : (^) -, - (^) 5, -2 (^) .. (^44) an = an : at (n-1)d the end of the d (^) --5 - (^) ) a1- 4tn -)d
#LP. whrch tetm of the
be - 82.
a HeaS on fott
-82.
d= -12 -}
an = - 82
any tcn youn
’ (^) Q+(n-)d = (^) -
-+ (n -)-5 - -
5n
a m
is
at(m-) d =^ -10^0
’(m-) -5 = -I00 7
Anrhmete
angett.
2 =4^ -5n^ + 5^ e-
te Ap? Gfve
-|.
n- = 15
aill
m
m = | 8.6+ la. 6 m i6 not a ohole no. S -100 îs not an Ap.
#LP Hous (^) many
105,112,|9 " a = 105
tmnee - digit numberS^ ane
an = 4q atCn-)d = qq
t05+7n -4 = q agt (^) tn (^) = (^444)
(aac
4LP: htch 4eHm^ of^ the 43,.., S the RMSt neqqi ve term?
het n' tenm be iaat negaive tem.
d 48 -
an <o ’ at (n-)d< ’ 53+^ (a^ -1)-5<
68-5n 0
I|.
#LP: the pth tem
is (p+ q, -n)
Qlp-1) d^ :4^ ’O
a+ (4-)d p’@
Substihuting
d in
CANd
an =^ Pt^ q-^ n LHS a + (n-)d
RHS = LHS
the
Gn (^) aat (^) (n-) d
teH ms 0f AP -
Sn [at given
19
find the 20h teHm
and finot Hnme
the frust (4 tems
= 150- 20
d^ (14-)^130
? xl&0^ t^ li4-)a]^1030
10 +(4-)a:1050^ at^
(n-nd
and nth tenm.
’ 10 t 19 X
Ean =?
then
1 2.
the Sum of frHSt a6 tenmS of the AP cohose nm tetm f8 given by an Qoth tenm to
Bax11 +(25- )6]
t 6n. AlSO
la. 5 x[2.+a4x6] Ia.5 x a3atI 12.5X 16G
Fas = a
find the Hatto OP 45 h term. an 5+6n
a4 = 5+6X
¡ -^ 5+^ bx 5+ 12
d 14 -||
and d : 6
11+ (20-) 11+ |qx
|25 a 20| n 45 aLg at(n-1)d]
11444 x 11 +
6TF an AP Qr :|644. find the value of k.
) Sn 3n +6n
S4 - 3x( +
:
S2 = 3x(2)+ 5X
C1 tQ2 22
a2 41
AE Sn 3n2t 5n and
14 -8 d
6 -
S
|a+{K-)d =\
6K I64- 6K = 62
The Sum of
ttms is 6L. Fnd the a8 th em of this
8n[2a+(n-)d]- 63
[Bxa+(7-1)a]- 63
laa +td-d] 63
?x0+3d = 63
= 63
63
d+a
Sa3 to ays = l6|
S8 =16I t 58 = 224
-ad-4a = 70
