JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q68

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The number of terms in an A.P. is even; the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by $10\frac12$ , then the number of terms in the A.P. is :

Answer and worked solution

Official answer: B

With $2k$ terms, $S_{even}-S_{odd}=kd=6$ . Also $(2k-1)d=\frac{21}2$ . Dividing: $\frac{2k-1}k=\frac74$ , so $k=4$ : 8 terms.

Topics:Arithmetic progression

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JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 68