Question

a11=38, a16=73,ap=? find the ap

Answer 1

Answer:

Ap = -12,-7,-2,3,7,......

Step-by-step explanation:

a11=38 a16=73

a11=a +10d | a16=a +15d

38= a+10d | 73 = a+15d

Applying elimination method.

a + 10d = 38

a + 15d = 73

- - -

_________

-5d = - 35

:- d = 5

Putting the value of d in any eq

a + 10d = 38

a + 10(5) = 38

a = 38 - 50

a = - 12

Now The ap will be:-

-12,-7,-2,3,7,..... (using formula a,a+d,a+2d,a+3d,....)

Hope u understand

Answer 2

a16 = 73

a11 = 38

We can write

a11 = a16 - 5D [D= Difference in terms]

38 = 73 - 5D

5D = 35

D = 7

We can write the 1st term a1 as,

a1 + 10D = a11

or, a1 + 70 = 38

a1 = -32

a2 = -25

a3 = -18

A.P = -32, -25, -18, -11, ......, 73

You can check the nth term using the formulla

an = a + (n-1) D

If 16th term is the nth term, we have

a16 = -32 + 15 x 7 = 105 - 32

a16 = 73