Question

In an AP if a=10 d=5 and n=100 then find the value of a100 and also find the 50th term from the end?

Answer 1

Answer (i)
the value of a100 is a + (n-1) d
a + (n-1) d = 100
10 + (n-1) 5 = 100
(n-1) 5 = 100-10 = 90
n-1 = 90/5 = 18
n-1 = 18
n. = 18+1 = 19

Answer (ii)
50th term of A. P. is a + (n-1) d. in this n. = 50
so, 50th term = a + (50-1) d
= a + 49 d
= 10 + (49) 5
= 10 + 245
= 255

Answer 2

Answer (i)

the value of a100 is a + (n-1) d

a + (n-1) d = 100

10 + (n-1) 5 = 100

(n-1) 5 = 100-10 = 90

n-1 = 90/5 = 18

n-1 = 18

n. = 18+1 = 19

Answer (ii)

50th term of A. P. is a + (n-1) d. in this n. = 50

so, 50th term = a + (50-1) d

= a + 49 d

= 10 + (49) 5

= 10 + 245

= 255