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Answer:
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Step-by-step explanation:
(1) AP:7,3,-1,-5.............
a=7,d=3-7=-4,n=20
an=a+(n-1)d
a20=7+(20-1)(-4)
=7+19(-4)
=7-76
a20 =-69
20th term of an A.P is -69
(2) common difference=a2-a1
a1=-0.2,a2=-0.3
a2-a1=-0.3-(-0.2)=-0.3+0.2=-0.1
common difference=-0.1
(3)d=-4,n=7,an=4
an=a+(n-1)d
4=a+(7-1)(-4)
4=a+(6)(-4)
4=a-24
a=24+4
a=28
(4) option c doesn't form an a.p
Because,The common difference between the terms is not same
(5)A.P=2,5,8,........,59
a=2,d=a2-a1=5-2=3,an=59
an=a+(n-1)d
59=2+(n-1)(3)
59=2+3n-3
59=-1+3n
3n=60
n=20
so, 20th term of the A.P is 59.
Hence there are 20 terms in the A.P
(6)a.p=√8,√18,√32
=2√2,3√2,4√2,5√2
Next term=50=√25×2=5√2
Next term=50
(7) First 20 natural numbers
1,2,3............,20
a=1, Last term(l)=20,n=20
sn=n/2(a+l)
=20/2(1+20)
=10(21)
=210
sum of first 20 natural numbers is 210
(8)a5=a10=71
a5=a+4d=71...,........(i)
a10=a+9d=71...........(ii)
(ii)-(i)
a+9d=71
a+4d=71
5d=0
d=0
subtitute'd=0' in 1st equation
a+4d=71
a+4(0)=71
a+0=71
a=71
a15=a+14d=71+14(0)=71+0=71
(9)d=5
a18=a+17d
a13=a+12d
a18-a13
a+17d-(a+12d)
a+17d-a-12d
17d-12d
17(5)-12(5)
85-60
=25
(10)A.P=3,15,27,39....
d=12
aK=a50+180
=a+49d+180
=3+49(12)+180
=3+558+180
=771