Sequences and Series: Inserting means MCQ

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Inserting meansMediumQuestion 210011

Question

The number of arithmetic means between 2 and 26 so that the ratio of 7th and 2nd means is 5:2 is:

If the common difference is d, $(2+7d)/(2+2d)=5/2$ gives $d=3/2$ . Also $d=(26-2)/(n+1)=24/(n+1)$ , so $n+1=16$ and n=15.