Question

the sum of 100 arithmetic means between 1 and 2 will be

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Numbers are 1 and 2}$

$\underline{\textsf{To find:}}$

$\textsf{Sum of 100 arithmetic means between 1 and 2}$

$\underline{\textsf{Solution:}}$

$\underline{\mathsf{Formula\;used:}}$

$\mathsf{Sum\;of\;n\;A.M.s\;between\;a\;and\;b=n{\times}A.M\;of\;a\;and\;b}$

$\implies\boxed{\mathsf{Sum\;of\;n\;A.M.s\;between\;a\;and\;b=n\left(\dfrac{a+b}{2}\right)}}$

$\mathsf{Now,}$

$\mathsf{Sum\;of\;100\;A.M.s\;between\;1\;and\;2=100{\times}A.M\;of\;1\;and\;2}$

$\mathsf{Sum\;of\;100\;A.M.s\;between\;1\;and\;2=100\left(\dfrac{1+2}{2}\right)}$

$\mathsf{Sum\;of\;100\;A.M.s\;between\;1\;and\;2=100\left(\dfrac{3}{2}\right)}$

$\mathsf{Sum\;of\;100\;A.M.s\;between\;1\;and\;2=100(1.5)}$

$\mathsf{Sum\;of\;100\;A.M.s\;between\;1\;and\;2=150}$

$\underline{\textsf{Answer:}}$

$\textsf{The sum of 100 A.M.s between 1 and 2 is 150 }$

$\underrline{\textsf{Find more:}}$

Insert three arithmetic means between -16 and 14

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Answer 2

Given :- the sum of 100 arithmetic means between 1 and 2 will be ?

Solution :-

Let A1, A2, A3, A4……An be N Arithmetic Means between two given numbers 1 and 2 .

Then 1, A1, A2 ….. An, 2 will be in Arithmetic Progression .

Now,

→ 2 = (N+2)th term of the Arithmetic progression .

So, we have,

• first term = a = 1
• last term = 2 .
• n = 100 + 2 = 102 .

then,

→ sum = (n/2)[first term + last term]

→ sum = (102/2)[ 1 + 2 ]

→ sum = 51 * 3

→ sum = 153

Therefore,

→ sum of arithmetic means between 1 and 2 = 153 - (1 + 2) = 153 - 3 = 150 (Ans.)

Learn more :-

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