Question

find the 7th term of the AP 1 by 4, 3 by 2 ,11 by 4

Answer 1

common difference is 1.25
first term is 1/4
7th term
= a+ (n-1) ×d
=1/4 + (7-1) ×1.25
=7.75

Answer 2

Answer:  The answer is $\dfrac{31}{4}.$

Step-by-step explanation:  Given arithmetic progression (A.P.) is

$\dfrac{1}{4},~\dfrac{3}{2},~\dfrac{11}{4},~.~.~.$

Here, first term 'a' is given by

$a=\dfrac{1}{4},$

and the common difference 'd' is given by

$d=\dfrac{3}{2}-\dfrac{1}{4}=\dfrac{11}{4}-\dfrac{3}{2}=\dfrac{5}{4}.$

We know that the n-th term is given by

$a_n=a+(n-1)d.$

Therefore, the 7-th term of the A.P. is

$a_7=a+(7-1)d=\dfrac{1}{4}+6\times\dfrac{5}{4}=\dfrac{1+30}{4}=\dfrac{31}{4}.$

Thus, the answer is $\dfrac{31}{4}.$