Question

Find n if the given value of x is the nth term of the given A.P.
(i)25,50,75,100...;x=1000
(ii)-1,-3,-5,-7,....;x=-151
(iii)5 1/2,11,16 1/2,22,...;x=550
(iv)121/11,31/11,41/11,...,x=171/11

Answer 1

(i)25,50,75,100...;x=1000         n = 40

(ii)-1,-3,-5,-7,....;x=-151                n = 76

(iii)5 1/2,11,16 1/2,22,...;x=550   n = 100

(iv)121/11,31/11,41/11,...,x=171/11   n = 17

We use the formula,

an = a + (n-1) d

(i)25,50,75,100...;x=1000

a = 25, d = 50-25 = 25 an = 1000

an = a + (n-1) d

1000 = 25 + (n-1) 25

975 = 25n - 25

1000 = 25n

n = 40

(ii)-1,-3,-5,-7,....;x=-151

a = -1, d = -3+1 = -2 an = -151

an = a + (n-1) d

-151 = -1 + (n-1) (-2)

-150 = -2n + 2

-152 = -2n

n = 76

(iii)5 1/2,11,16 1/2,22,...;x=550

a = 5, d = 11 - 5 1/2 = 11/2 an = 550

an = a + (n-1) d

550 = 5 1/2 + (n-1) 11/2

550 - 11/2 = 11/2n - 11/2

550 = 11/2n

n = 100

(iv)1, 21/11,31/11,41/11,...,x=171/11

a = 1, d = 31/11-1 = 10/11 an = 171/11

an = a + (n-1) d

171/11 = 1 + (n-1) (10/11)

171 = 11 + (n-1) (10)

160 = 10n - 10

170 = 10n

n = 17