Sequences & SeriesmediumPYQ · JEE Main · 5 Apr 2026 · Shift 2 (Afternoon)Free

Sequences & Series: Let Arithmetic Means Between Mean Equal (JEE Main 2026)

JEE Maths question with a full step-by-step solution.

Question

Let

A_1, A_2, \ldots, A_{39}

be 39 arithmetic means between 59 and 159. Then the mean of

A_{25}

A_{28}

A_{31}

and

A_{36}

is equal to:

129

136

131.50

134

correct

Solution

Step 1: Determine the common difference The sequence

59, A_1, A_2, \ldots, A_{39}, 159

has

41

terms, so:

d = \frac{159-59}{40} = \frac{100}{40} = \frac{5}{2}

Step 2: Evaluate each required arithmetic mean using

A_k = 59 + k\cdot\dfrac{5}{2}

A_{25} = 59+\frac{125}{2} = 121.5, \quad A_{28} = 59+70 = 129, \quad A_{31} = 59+\frac{155}{2} = 136.5,

and

A_{36} = 59+90 = 149

Step 3: Compute the mean For an arithmetic progression, the mean of a set of terms equals the term at the mean index. Mean index

= \dfrac{25+28+31+36}{4} = 30

\text{Mean} = A_{30} = 59+30\cdot\frac{5}{2} = 59+75 = 134

Direct verification:

\dfrac{121.5+129+136.5+149}{4} = \dfrac{536}{4} = 134

\checkmark

Answer: (4)

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