Question

if the fifth term of an ap is 23 and seventh term is 33 find sixteenth term

Answer 1

this is your answer
$a + 4d = 23 \\ a + 6d = 33 \\ on \: solving \: the \: eqution \: we \: get \: \\ a = 3 \: and \: d = 5 \\ so \: sixteenh\: term \: is \: a + 15d \: = 3 + 5 \times1 5 \\ = 78$

Answer 2

a5=23
a7=33
a16=?
a+4d=23. 1
a+6d=33. 2
by elimination method
d=5
now
put d=5 in eq 1
a=3
a16=a+15d
a16=3+15.5
a16= 78