Question

find the 31st term of an AP,whose 11th term is 38 and 16th term is 73​

Answer 1

n=11

an=38

38=a+(11-1)d

38=a+10d

now n=16

an=73

an=a+(n-1)d

73=a+(16-1)d

73=a+15d

by eliminating them,

38=a+10d

73=a+15d

- - -

_________

-35=-5d

35=5d

d=7

putting values of d

38=a+10d

38=a+10(7)

38-79=a

-41=a

now we have to find 31st term

n=31

an=a+(n-1)d

an=-41+(31-1)7

an=-41+(30)7

an=-41+210

an=169