Question

On the number line above, the tick marks are equally spaced and their coordinates are shown. Of these coordinates, which has the smallest positive value?

• A. $a$
• B. $b$
• C. $c$
• D. $d$
• E. $e$

Answer 1

The correct option is C $c$

Given

Number of terms in arithmetic progression $=$ $7$

First term ofarithmetic progression $=$ $-8$

We know that

$n^{th}$ term of the arithmetic progression $=$ $a$ $+$ $(n$ $-$ $1)d$,

where, $a$ is the first term of arithmetic progression

$d$ is the common difference of the arithmetic progression

To find ${}^{\prime }{d}^{\prime }$$\left(commondifferenceofAP\right)$,

$7^{th}$ term ofarithmetic progression $=$ $10$

$a$ $+$ $(n$ $-$ $1)d$ $=$ $10$

Here, $a$ $=$ $-8$ and $n$ $=$ $7$

$-8$ $+$ $(7$ $-$ $1)$ $d$ $=$ $10$

$-8$ $+$ $6d$ $=$ $10$

$6$ $\times$ $d$ $=$ $10$ $+$ $8$

$d$ $=$ $\frac{18}{6}$

$d$ $=$ $3$

Hence, the terms of $AP$ are

$-8,$ $-5,$ $-2,$ $1,$ $4,$ $7,$ $10$

${}^{\prime }{1}^{\prime }$ has the smallest positive value in the list.

If we compare these terms with the given real line,

$a$ $=$ $-5,$ $b$ $=$ $-2,$$c$ $=$ $1,$ $d$ $=$ $4,$ $e$ $=$ $7$

Therefore, ${}^{\prime }{c}^{\prime }$ has the smallest positive value.