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The value of x + y + z is 15, if a, x, y, z, b are in A.P. The

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The value of $x + y + z$ is $15$ , if $a, x, y, z, b$ are in A.P. Then find $a + b$

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The value of

x + y + z

15

, if

a, x, y, z, b

are in A.P. Then find

a + b

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Let A.P. have first term

a

and common difference

d

\Rightarrow x = a + d, y = a + 2 d, y = a + 3 d, b = a + 4 d

We have,

x + y + z = 15 \Rightarrow 3 a + 6 d = 15 \Rightarrow a + 2 d = 5 \Rightarrow (1)

Hence

a + b = a + (a + 4 d) = 2 a + 4 d = 2 (a + 2 d) = 2 (5) = 10

using (1)

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Question Text	The value of $x + y + z$ is $15$ , if $a, x, y, z, b$ are in A.P. Then find $a + b$
Answer Type	Text solution:1
Upvotes	150