Let be 39 arithmetic means between the numbers 59 and 159. Then the mean of and is equal to: [2026]

Question

Let $A_{1}, A_{2}, A_{3}, . . ., A_{39}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of $A_{25}, A_{28}, A_{31}$ and $A_{36}$ is equal to: [2026]

Smart Achievers · Accepted Answer

(4)

Given 39 arithmetic means between 59 and 159.

So, sequence is $59, A_{1}, A_{2}, A_{3}, . . ., A_{39}, 159$ , (4! terms)

Common difference, $d = \frac{159 - 59}{40} = \frac{100}{40} = \frac{5}{2}$

$∴ A_{k} = 59 + k \cdot (\frac{5}{2})$

$∴ A_{25} = 59 + 25 (\frac{5}{2}) = 121.5$

$A_{28} = 59 + 28 (\frac{5}{2}) = 129$

$A_{31} = 59 + 31 (\frac{5}{2}) = 136.5$

$A_{36} = 59 + 36 (\frac{5}{2}) = 149$

$∴ Mean = \frac{121.5 + 129 + 136.5 + 149}{4} = 134$

Solution

Q.
Let $A_{1}, A_{2}, A_{3}, . . ., A_{39}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of $A_{25}, A_{28}, A_{31}$ and $A_{36}$ is equal to: [2026]

1 129

2 136

3 131.5

4 134

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