Question

same question it is emergency please check it out

Answer 1

here is your answer mate hope its helpful

Answer 2

The Answer is Written Below, I am only answering the question no: 6, 9, 11, 14, 16

question 6) Prove that -150 is an A.P of the team

a= 11 ,d= -3

so, an=a+(n-1)d

-150 = 11 + (n-1)-3

-150 = 11 -3n + 3

-150 - 14 = -3n

-164 = -3n

n=164/3 (it is not possible an nth term to be in decimal)

So, -150 isn't the AP of term

Question 9) 3rd term of AP = 4 , 9th term of AP = - 8

a + 2d = 4 ,

a + 8d = -8

(-)   (-)     (+)

    -6d=12

d= -2

a+2d= 4

a+ 2(-2)=4

a -4 =4

a=8, d=-2

So, we are told to find the nth term which we be 0(An)

0= 8 (n-1)-2

0= 8 -2n + 2

-10 = -2n

n=5 (5th term will be 0)

Question 11) a=3 d= 12

find the value of an of 54th term

an = 3+53(12)

an = 3+ 636

an=639

Now, they want to know that is term which will be 132 more than 639

So, add them 639+132 =771

an=771

find the nth term of 771

771 = 3 (n-1)12

771 = 3 -12 +12n

771= -9 +12n

780 = 12n

n= 780/12

n= 65

Question 14) The how many number lie between 10 and 250

firstly, 10 isn't the multiple of 4, but 12 is the multiple of 4

so a= 12 (given that find the multiple of 4 between 10-250 so, d=4)

similarly 250 isn't the multiple of 4, 248 is...

last term is 248

now, 248 = 12(n-1)4

248 = 12 +4n -4

248 = 8 +4n

240 = 4n

n= 60

60 term are there between 10-250 which are multiple of 4

Question 16) third term is 16 and 7th term is 12 more than 5th term

a+2d = 16

a+6d = a+4d +12

a+6d -a -4d = 12

2d=12

d=6

a+2d=16

a+2(6)=16

a+12=16

a=4

and, the AP is 4,10,16,22,28......

Regards :)