Question

if 12th term of an A.P. is -13 and the sum of first four terms is 24 , what is the sum of first 10 terms ? is -150 a term of the A.P. 11,8,5,2....?​

Answer 1

In The first part of the question the value of d comes out to be -2

This can be done by solving two equations, a+11d= -13
And 2(a+3d)=24 [sum formula of a.p]

Now a+11d =-13

Put d=-2

You will get a= 9

Now put this value of a in the equation used to find sum of n terms i.e s = n/2 [2a+(n-1)d]

n=10 and d= -2

You will get s= 0

Hope this helped you,please thank this answer and mark this answer as brainiest answer if you understood

Answer 2

Answer:

Given - a12=-13 and S4=24,an=-150

To find - S10=?

-150 a term of 11,8,5,2,...

Step-by-step explanation:

a12=-13

=>a+11d=-13______(i)

S4=24

=>n/2(2a+(n-1)d)=24

=>4/2(2a+(4-1)d)=24

=>2a+3d=12_________(ii)

Form (i)

a=-13-11d________(iii)

Put (iii) in (ii)

=>2*(-13-11d)+3d=12

=>-26-22d+3d=12

=>22d-3d=-26-12

=>19d=-38

=>d=-2

Put value of d in (i)

=>a+11*(-2)=-13

=>a=22-13

=>a=9

S10=10/2(2*9+9*(-2))

=>5(18-18)

S10=0

So Sum of 10 number is 0

11,8,5,2,...

a=11, d=-3

=>an=-150

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

-3n=-164

n=164/3

So -150 is not an term of AP