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Standard X

Mathematics

Relation between Terms, Their Position and Common Difference

If the sum of...

Question

If the sum of the first $n$ terms of an AP is $5 n - n^{2}$ , the common difference is ______

-2

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Solution

The correct option is D
2

$S_{n} = 5 n - n^{2}$

$T_{1} = S_{1} = 5 (1) - (1)^{2} = 5 - 1 = 4$

$S_{2} = T_{1} + T_{2} = 5 (2) - (2)^{2} = 10 - 4 = 6$

$T_{2} = S_{2} - T_{1} = 6 - 4 = 2$

$d = T_{2} - T_{1} = 2$

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If the sum of the first n terms of an AP is 5n−n2, the common difference is ______

The correct option is D 2 Sn=5n−n2 T1=S1=5(1)−(1)2=5−1=4 S2=T1+T2=5(2)−(2)2=10−4=6 T2=S2−T1=6−4=2 d=T2−T1=2

If the sum of the first $n$ terms of an AP is $5 n - n^{2}$ , the common difference is ______

The correct option is D
2

$S_{n} = 5 n - n^{2}$

$T_{1} = S_{1} = 5 (1) - (1)^{2} = 5 - 1 = 4$

$S_{2} = T_{1} + T_{2} = 5 (2) - (2)^{2} = 10 - 4 = 6$

$T_{2} = S_{2} - T_{1} = 6 - 4 = 2$

$d = T_{2} - T_{1} = 2$