1(viii)
The 7th term of the given Arithmetic Progression (A.P.):
$\frac{1}{a}, \Big(\frac{1}{a} + 1\Big), \Big(\frac{1}{a} + 2\Big), ......$ is :
- (a)$\Big(\frac{1}{a} + 6\Big)$
- (b)$\Big(\frac{1}{a} + 7\Big)$
- (c)$\Big(\frac{1}{a} + 8\Big)$
- (d)$\Big(\frac{1}{a} + 7^7\Big)$
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In the A.P. :
$\frac{1}{a}, \Big(\frac{1}{a} + 1\Big), \Big(\frac{1}{a} + 2\Big), ......$
First term (x) = $\frac{1}{a}$
Common difference (d) = $\frac{1}{a} + 1 - \frac{1}{a}$ = 1.
x7 = x + (7 - 1)d
= $\frac{1}{a} + 6 \times 1$
= $\Big(\frac{1}{a} + 6\Big)$.
Hence, Option 1 is the correct option.