Question

THE AVERAGE OF 15 RESULTS IS 28 THE AVERAGE OF THE FIRST 7 IS 26 AND THAT OF THE LAST 7 IS 25 FIND THE VALUE OF THE 8TH NUMBER ​

Answer 1

Answer:

8th term = 63 .

Step-by-step explanation:

Given :- 1. avg. of 15 numbers = 28 ,

             2. avg. of first 7 numbers = 26

             3. avg. of last 7 numbers = 25

To find :- Value of 8th number .

Solution :-

Step 1) Let , $n_1 , n_2 , n_3 ......n_{15}$ be the numbers .

Step 2) Given , average of 15 numbers is 28 ,

$\frac{n_1 + n_2 + n_3 ..... + n_{15}}{15} = 28 \\n_1 + n_2 + n_3 ....+ n_{15} = 28*15 = 420 .$ -----(1)

Step 3) Average of first 7 numbers is 26 ,

$n_1 + n_2 ..... + n_7 = 26$

$\frac{n_1+n_2+n_3 ......n_7}{7} = 26 \\n_1 + n_2 + n_3 + ...... + n_7 = 26*7 = 182$ ----- (2)

Step 4) Average of last 7 terms is 25 ,

$\frac{n_9 + n_{10} + n_{11} ....... + n_{15}}{7} =25\\\\n_9 + n_{10} + ..... + n_{15} = 25*7 = 175$ ----- (3)

Step 5) From equation (1) , (2) , (3)  we get

$182 + n_8 + 175 = 420 \\n_8 = 420 - 182 - 175 \\n_8 = 63$

Therefore ,

Answer is $n_8 = 63$ , i.e. 8th term = 63 .

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