Consider the following AP: 1, a, b, c, 9. Find the common difference.

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Solution

The correct option is D
2

The formula to find the $n^{t h}$ term of an arithmetic progression is $t_{n} = a_{1} + (n - 1) d$ .

where,

' $a_{1}$ ' is the first term,

'd' is the common difference,

'n' is the no. of terms,

' $t_{n}$ ' is the $n^{t h}$ term.

There are five terms in this AP. i.e., n = 5

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

$\Rightarrow$ $a_{n} - a_{1} = (n - 1) d$

$\Rightarrow$ $\frac{a_{n} - a_{1}}{n - 1} = d$

Given, $a_{1} = 1; n = 5; a_{n} = 9$ .

Therefore the common difference, $d = \frac{9 - 1}{5 - 1} = 2$

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