Question

find the common difference of an AP whose first term is 1/2 and the 8th term is 17/6 also find its 4th term.

Answer 1

17/6 = 1/2 + 7d
17/6-1/2 = 7d
7/3 = 7d
d = 1/3

a4 = 1/2 + 3*1/3
= 1/2 + 1
= 3/2

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Answer 2

The common difference of an AP between 1/2 and 17/6 is 1/3 and the fourth term is 3/2

Solution:

The common difference is equals to subtraction of 8th value and 1st value. i.e., (8-1)d = (8d-1d)

From the given data and known value,

$(8 d-1 d)=7 d \Rightarrow \frac{17}{6}-\frac{1}{2}$

$7 d=\frac{17}{6}-\frac{3}{6}$

$7 d=\frac{14}{6}$

$7 d=\frac{7}{3}$

$\Rightarrow d=\frac{1}{3}$

In AP, 4th term will be,

$a_{4} = a + (n - 1) d$

$a_{4} = \frac{1}{2}+(4-1)\left(\frac{1}{3}\right)$

$a_{4} = \frac{1}{2}+3\left(\frac{1}{3}\right)$

$a_{4} = \frac{1}{2}+1$

$a_{4} = \frac{3}{2}$