JEE Main 2022 · 28 Jun · Shift 2 · Mathematics Q5

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MathematicsSingle correct+4 / -1Question 5 of 90

If $n$ arithmetic means are inserted between $a$ and 100 such that the ratio of the first mean to the last mean is $1:7$ and $a+n=33$ , then the value of $n$ is :

Answer and worked solution

Official answer: C

Means. With $d=\frac{100-a}{n+1}$ : $7(a+d)=100-d$ , so $7a+8d=100$ .

Use $a=33-n$ . $(131-7n)(n+1)+8(67+n)=0$ , i.e. $7n^2-132n-667=0=(n-23)(7n+29)$ , so $n=23$ .

(C)

Topics:Arithmetic progression

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JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 5