Solution of equation (x + 1) + (x + 4) + (x + 7) + ......... + (x + 28) = 155 is

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8. Sequences and Series

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The solution of the equation $(x + 1) + (x + 4) + (x + 7) + ......... + (x + 28) = 155$ is

A

$1$

B

$2$

C

$3$

D

$4$

Solution

(a) We have $(x + 1) + (x + 4) + ……… + (x + 28) = 155$

Let $n$ be the number of terms in the $A.P.$ on $L.H.S.$

Then $x + 28 = (x + 1) + (n – 1)3$

$ \Rightarrow $ $n = 10$

$\therefore $ $(x + 1) + (x + 4) + …… + (x + 28) = 155$

$ \Rightarrow $ $\frac{{10}}{2}[(x + 1) + (x + 28)] = 155$

$ \Rightarrow $ $x = 1$.

Standard 11

Mathematics

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