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Rd Chapter 9 Arithmetic Progressions Ex 9.6 Solutions

Question - 11 : -
Find the sum of the first
(i) 11 terms of the A.P. : 2, 6, 10, 14,…
(ii) 13 terms of the A.P. : -6, 0, 6, 12,…
(iii) 51 terms of the A.P.: whose second term is 2 and fourth term is 8.

Answer - 11 : -


Question - 12 : -
Find the sum of
(i) the first 15 multiples of 8
(ii) the first 40 positive integers divisible by
(a) 3, (b) 5, (c) 6
(iii) all 3-digit natural numbers which are divisible by 13. [CBSE 2006C]
(iv) all 3-digit natural numbers, which are multiples of 11. [CBSE 2012]
(v) all 2-digit natural numbers divisible by 4. [CBSE 2017]

Answer - 12 : -


Question - 13 : -
Find the sum :
(i) 2 + 4 + 6 + ……….. + 200
(ii) 3 + 11 + 19 + ………. + 803
(iii) (-5) + (-8) + (-11) + ……. + (-230)
(iv) 1 + 3 + 5 + 7 + …….. + 199
(v) 7 + 10(1/2) + 14 + ……… + 84
(vi) 34 + 32 + 30 + ………. + 10
(vii) 25 + 28 + 31 + ……….. + 100 [CBSE 2006C]
(viii) 18 + 15(1/2) + 13 + ……… + (-49(1/2))

Answer - 13 : -


Question - 14 : - The first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum ?

Answer - 14 : -

First term of an A.P. (a) = 17
Last term (l) = 350
Common difference (d) = 9
Let n be the number of terms Then an = a + (n – 1) d
=> 350 = 17 + (n – 1) x 9
=> 350 = 17 + 9n – 9
=> 9n = 350 – 17 + 9 = 342
n = 38
Number of terms = 38
Now Sn = (n/2) [a + l]
= (38/2) [17 + 350] = 19 (367) = 6973

Question - 15 : - The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.

Answer - 15 : -


Question - 16 : - The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

Answer - 16 : -


Question - 17 : - If 12th term of an A.P. is -13 and the sum of the first four terms is 24, what is the sum of first 10 terms ?

Answer - 17 : -

12th term of an A.P. = -13
Sum of first 4 terms = 24
Let a be the first term and d be the common difference

Question - 18 : - Find the sum of n terms of the series

Answer - 18 : -


Question - 19 : - In an A.P., if the first term is 22, the common difference is -4 and the sum to n terms is 64, find n.

Answer - 19 : -


Question - 20 : - In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms ?

Answer - 20 : -

In an A.P.
5th term = 30

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