Question

the 11th term and 21st term of ap is 16&29.finf the 1) 1st term
2) the 34th term
3) n=such that tn=55​

Answer 1

a + 10d = 16 ...............(1)

and

a + 20d = 29 ..............(2)

solving eq. 1 and 2

a + 10d = 16

a + 20d = 29

__________

-10d = - 13

d = 1.3

from eq 1 we get

a = 16 - 10d

a = 16 - 13

a = 3

T 34 = 3 + 33 x 1.3

= 3 + 42.9

= 45.9

Tn = 55

=> 3 + 1.3n - 1.3 = 55

=> 1.3n = 55 - 1.7

=> n = 53.3/13

=> n = 41

1) 1st term = 3

2) the 34th term = 45.9

3) n=such that tn=55 = 41