Question

If 6 arithmetic means are inserted between the numbers 3 and 66, then the fourth arithmetic mean is equal to _____. CORRECT ANSWER WILL BE MARKED AS BRAINLIEST.

Answer 1

${\huge {\mathbb { Answer :-}}}$

$\boxed {Method-1}$

The series becomes :

3, 3 + d, 3 +2d,..., 3 + 6d, 66

So, 66 = 3 + 7d

or, 7d = 63

or, d = 9.

.°. Fourth mean = 3 + 4d = 3 + 36 = 39

$\boxed {Method-2}$

Use formulae,

If n arithmetic means are inserted between a and b, then we can say :

◼️d = (b - a) / (n + 1)◼️

So, d = (66 - 3) / 7 = 9

.°. 4th mean = 3 + 4×9 = 39

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Answer 2

Answer:

Answer:−

\boxed {Method-1}

Method−1

The series becomes :

3, 3 + d, 3 +2d,..., 3 + 6d, 66

So, 66 = 3 + 7d

or, 7d = 63

or, d = 9.

.°. Fourth mean = 3 + 4d = 3 + 36 = 39

\boxed {Method-2}

Method−2

Use formulae,

If n arithmetic means are inserted between a and b, then we can say :

◼️d = (b - a) / (n + 1)◼️

So, d = (66 - 3) / 7 = 9

.°. 4th mean = 3 + 4×9 = 39