Question

Find the 31 term of and AP whose 11 term is 38 and 16 term is 73

Answer 1

11th term = a + 10d.
and,16th term = a + 15d
then,

A.T.Q, a+15d=73. (1)
a+10d=38. (2)

subtract (1) by (2),we get
5d=35
{d=7}

from (1)
a+15×7=73
a=73-105
{a=-32}

NOW WE HAVE 1st term,common difference and n. So,
an = a+(n-1)d
an = -32+(30)7
an = -32+210

【an = 178】

【【☺️HOPE IT WILL HELP YOU】】

Answer 2

for ap,

11 term=38

a+10d=38.......(1)

16 term=73

a+15d=73......(2)

subtract(1)from(2)

a+15d-(a+10d)=73-38

a+15d-a-10d=35

5d=35

d=7

put the value of d in eq(1)

a+10(7)=38

a=38-70

a= -32

31term = a+30d

= -32+30(7)

=178

hope it helps uu✌✌