If sum of 10 terms of an A.P. is 4 times to sum of its 5 terms, then ratio of first term and common

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8. Sequences and Series

easy

If the sum of the $10$ terms of an $A.P.$ is $4$ times to the sum of its $5$ terms, then the ratio of first term and common difference is

A

$1:2$

B

$2:1$

C

$2:3$

D

$3:2$

Solution

(a) Under conditions, we get

$\frac{{10}}{2}\left\{ {2a + (10 – 1)d} \right\} = 4\left[ {\frac{5}{2}\left[ {2a + (5 – 1)d} \right]} \right]$

$ \Rightarrow $$2a + 9d = 4a + 8d$ or $\frac{a}{d} = \frac{1}{2}$

Hence $a:d = 1:2$.

Standard 11

Mathematics

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