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The sequence P1,P2,P3..... satisfies the...

The sequence `P_1,P_2,P_3.....` satisfies the relation `2P_n=P_(n-1)+P_(n+1)` where ` n >1.` Given that `P5=26 and P7=38,` find the values of `P90 and P90+P50` a. 1436 b. 1070 c. 536 d. 832

Text Solution

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Here, `2P_n = P_(n-1)+P_(n+1)`
`P_n = (P_(n-1)+P_(n+1))/2`
Thus, given sequence is an `AP`.
`:. a+4d = 26->(1)`
`a+6d = 38->(2)`
Subtracting these two equations,
`a+6d-a-4d = 38-12=> 2d = 12=> d = 6`
`:. a +4(6) = 26=> a = 26-24 = 2`
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