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Algebra Level 1

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

{ a }_{ 60 }

{ a }_{ 56 }

{ a }_{ 49 }

{ a }_{ 38 }

2 solutions

Harsh Shrivastava
Mar 15, 2015

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 $a_{56}$

$\boxed {\huge \text {CORRECT ! }}$

Vaibhav Prasad - 6 years, 3 months ago

Congrats on $119$ followers!!

Harsh Shrivastava - 6 years, 3 months ago

But u got 600 followers man !!!!!! Ur awesome

Vaibhav Prasad - 6 years, 3 months ago

Harsh Shrivastava - 6 years, 3 months ago

@Harsh Shrivastava – allright enough

Vaibhav Prasad - 6 years, 3 months ago

Which paper did you had today??

Harsh Shrivastava - 6 years, 3 months ago

Siddharth Singh
Mar 18, 2015

Find the mean of the series by, S/111=n/2[2a+(n-1)]/111. Find the term which is equal to the mean by: mean=a+(n-1)d