Question

Find k if the given value of x is the kth term of Ap and x= 550

Answer 1

Your question is incomplete, But as i know the question already.

Here is your answer:

The AP is:

5.5,11,16.5,22.........  and x =  550

∴ d = 11-5.5 = 11/2 = 5.5

   a = 5.5

An = a+(n-1)d

An= 5.5+(n-1)5.5

An= 5.5 + 5.5n - 5.5

An= 5.5n

∴ 550 = 5.5n

n = 550/5.5

n = 100

Thus, 100th term of the AP is 550  (x=550)

Answer 2

$\huge{\bold{Answer}}$

Complete Question=>

>Find k if the given value of x is the kth term of Ap 5$\frac{1}{2}$, 11, 16$\frac{1}{2}$,22.. and x= 550

The Given AP^^

5$\frac{1}{2}$, 11, 16$\frac{1}{2}$,22..

a = 5$\frac{1}{2}$= $\frac{11}{2}$

let a1 = $\frac{11}{2}$

a2 = 11

difference, d= a2 - a1= 11 - $\frac{11}{2}$

d = $\frac{22-11}{2}$

d = $\frac{11}{2}$

(last term) T(n) = x = 550

T(n) = a + (n-1)d

550 = $\frac{11}{2}$ + (n-1)$\frac{11}{2}$

550 - $\frac{11}{2}$ = (n-1)$\frac{11}{2}$

$\frac{1100-11}{2}$ = (n-1)$\frac{11}{2}$

$\frac{1089}{2}$ = (n-1)$\frac{11}{2}$

1089 = (n-1)11

(n-1) = $\frac{1089}{11}$

(n-1)= 99

n = 100

therfore, x=550 is the 100th term of the given AP..