Let {S₁},{S₂},......,{S_{101}} be consecutive terms of an A.P . If frac{1}{{{S₁}{S?

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8. Sequences and Series

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Let ${S_1},{S_2},......,{S_{101}}$ be the consecutive terms of an $A.P$ . If $\frac{1}{{{S_1}{S_2}}} + \frac{1}{{{S_2}{S_3}}} + .... + \frac{1}{{{S_{100}}{S_{101}}}} = \frac{1}{6}$ and ${S_1} + {S_{101}} = 50$ , then $\left| {{S_1} - {S_{101}}} \right|$ is equal to

A

$10$

B

$20$

C

$30$

D

$40$

Solution

Using properties of $A.P$.,

we get $|S_1 – S _{101}| = 10$

Standard 11

Mathematics

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