$a_1, a_2, a_3, \ldots , a_{111}$ follow an arithmetic progression. What will be their arithmetic mean?

Given that
${ a }_{ 60 }$
${ a }_{ 56 }$
${ a }_{ 49 }$
${ a }_{ 38 }$

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Let common difference be $x$ . We re-write the series as $a_{1}, a_{1} + x , a_{1} + 2x, a_{1} + 3x, . . . . . . . . . , a_{1} + 110x$ .

Now adding them, we get $111a_{1} + 6105x$ .

Dividing them by $111$ , we get $a_{1} + 55x$ , which is their arithmetic mean.

$'a_{i}'$ th term is given by $a_{i} = a_{1} + (i-1)x$

Hence by comparing , we get our answer as $a_{56}$