Question

the 8th term of A.P is 17 and the 19th term is 39. find the 25th term=______

a) 51

b) 61

c)65

d)55

please answer with solved

Answer 1

let the first term is a and diff.... is d
then
according to the question
a + 7d=17



a+18d=39
a+7d+11d=39
17 + 11d=39
11d=22
d=2

a=17-7×2=3



a+24d=3+24×2=51

Answer 2

Given,

$t_{8} = 17 \\ \\ a + 7d = 17 - - - (i) \\ \\ \\ t_{19} = 39 \\ \\ a + 18d = 39 - - - (ii)$


From i and ii

follow the attachment above


From i

a + 7d = 17
=> a + 7 × 2 = 17
=> a = 17 - 14
=> a = 3

Given,

a = 3
d = 2

$t_{25} = a + (n - 1)d \\ \\ = 3 + (25 - 1)2 \\ \\ = 3 + 24 \times 2 \\ \\ = 3 + 48 \\ \\ = 51$


$\huge \bold {51}$