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**Q.1. Find the sum of two middle most terms of the A.P. Ans.** Here a = -4/3

â‡’

â‡’

â‡’

â‡’ n -1 = 17

â‡’ n = 18

âˆµ n = 18 (even)

âˆ´ Middle terms are

i.e. 9th and 10th term

Now, sum = a

= a + 8d + a + 9d

= 2 a + 17 d

So, the sum of two middle most terms = 3

(i) divisible by 9. (ii) not divisible by 9.

[Hint (ii): These numbers will be: Total numbers - Total numbers divisible by 9]

Ans.

Here, a = 108, d = 9, a

a

â‡’ 198 = 108 + (n - 1)9

â‡’ 198 = 108 + 9n - 9

â‡’ 198 = 99 + 9n

â‡’ 198 - 99 = 9n

â‡’ 99/9 = n â‡’ 11 = n

and

(ii) Numbers between 100 and 200 are 101,102,..., 199

a = 101, d = 1, a

âˆ´ a

âˆ´

âˆ´ Sum of numbers not divisible by 9

= 14850 - 1683 = 13167.

Ans.

â‡’

Subtracting (i) and (ii), 2a + 5d = 12

Ans.

âˆ´ Piggy bank amount = â‚¹ 496

Amount spent = â‚¹ 204

Amount left = â‚¹ 100

Total pocket money = â‚¹ 800

Ans.

Multiplying equation (ii) by 6 and then subtracting from

(i), we have

= 10 [2 x 1 + 19 x 5]

= 10 [2 + 95] = 10 x 97 = 970

Ans.

Middle most term =

Hence AP becomes 4, 8, 12, 16, ..... , 52

a = 4, d = 4, a

âˆ´

and distance covered to collect the books = 364 m

âˆ´ Total distance covered = 364 + 364 = 728 m

Maximum distance she travelled carrying a flag is 26 m.

Ans.

Ans.

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