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Answers
In case of 4 terms, we usually take 2d as the common difference and the average of the two middle terms should be a.
Therefore, Let a-3d, a-d, a+d and a+3d be the 4 terms.
Now, By Question, we have
(a-3d) + (a-d) + (a+d) + (a+3d) = 32
=> 4a = 32
=> a = 8
Again, By Question, we have
(a-3d)*(a+3d) : (a-d)*(a+d) = 7 : 15
=> a^2 - 9d^2 : a^2 - d^2. = 7 : 15
=>15(a^2 - 9d^2) = 7(a^2 - d^2)
=>15a^2 - 135d^2. = 7a^2 - 7d^2
=>15a^2 - 7a^2. = 135d^2 - 7d^2
=>8a^2. = 128d^2
=>8(8)^2. = 128d^2 (Substituting the value of a)
=>512. = 128d^2
=>4. = d^2
=>d =(+)(-)2
Therefore Common Difference = 2d = (+)(-)4
Therefore, The required AP is -
a-3d = 8 - 3(2) = 2. Or. a-3d = 8-3(-2) = 14
a-d. = 8 - 2. = 6. Or. a-d. = 8-(-2) = 10
a+d. = 8+2. = 10. Or. a+d. = 8+(-2) = 6
a+3d = 8+3(2) = 14. Or. a+3d = 8+3(-2) = 2
Answer:
Step-by-step explanation:thats the answer your welcome
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