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Question

In an AP:
(i) Given a=5,d=3,an=50, find n and Sn.
(ii) Given a=7,a13=35, find d and S13.
(iii) Given a12=37,d=3, find a and S12.
(iv) Given a13=15,S10=125, find d and a10.

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Solution

(i) Given a=5,d=3,an=50, find n and Sn .

an=a+(n1)d

50=5+(n1)3

15=n1

n=16

Sn=n2[2a+(n1)d]

=162[2(5)+(161)3]

=8×55

Sn=440

(ii) Given a=7,a13=35 , find d and S13

an=a+(n1)d

35=7+(131)d

28=12d

d=73

Sn=n2[a+l]

=132[7+35]

=273

S13=273

(iii) Given a12=37,d=3, find a and S12

an=a+(n1)d

37=a+(121)3

3711×3=a

a=4

Sn=n2[a+l]

=122[4+37]

=246

S12=246

(iv) Given a13=15,S10=125,find d and a10

an=a+(n1)d

15=a+(131)3

15=a+12d...(1)

Sn=n2[2a+(n1)d]

125=102[2a+(101)d]

25=2a+9d...(2)

Solving (1) and (2), we get,

d=1,a=17

an=a+(n1)d

a10=17+(101)(1)

=179=8

a10=8

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