Answer :

Let 8^{th} observation be x

Mean of first 8 observations = 18

where K is sum of first 7 terms

x = 144 – k ..(i)

Mean of last 8 observations = 20

Where L is sum of last 7 terms

x = 160 – L ..(ii)

Equating both the equations

160 – L = 144 – K

16 + K = L ..(iii)

Mean of all 15 terms = 19

K + X + L = 285

From equation (i), (ii), (iii)

K + (144-K) + (16 + K) = 285

⇒ K = 125

Replacing value in equation (i)

We get x = 19

So, 8^{th} term is 19

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