NCERT Solutions For Class 10 Math Chapter – 5 Exercise – 5.2
Q1. Fill in the blanks in the following table , given that a is the first term , d the common difference and an the nth term of the A.P:
| A | D | N | AN |
| 7 | 3 | 8 | …. |
| -18 | …… | 10 | 0 |
| -18.9 | 2.5 | ….. | 3.6 |
| ….. | -3 | 18 | -5 |
| 3.5 | 0 | 105 | …. |
Solution:-
| A | D | N | AN |
| 7 | 3 | 8 | 28 |
| -18 | 2 | 10 | 0 |
| -18.9 | 2.5 | 10 | 3.6 |
| 46 | -3 | 18 | -5 |
| 3.5 | 0 | 105 | 3.5 |
Q2. Choose the correct choice in the following and justify:
- 30thterm of the AP: 10 , 7 , 4 …… , is
- 97 (b) 77 © -77 (d) -87
- 11th term of the A.P. -3 , -1/2 , 2 , ….., is
- 28 (b) 22 © -38 (d) – 97/2
Solution:-
- -77
- 22
Q3. In the following APs find the missing the terms in the boxes:
- 2, _____ , 26
- ______, 13 , ______ , 3
- 5 , ______ , ______ , 19/2
- -4 , ______ , _______ , _______ , _____ , 6
Solution:-
- 14
- 18 , 8
- 13/2 , 8
- -2 , 0 , 2 , 4
Q4. Which term of AP: 3 , 8 , 13 , 18 ……., is 78 ?
Solution:-
Let an = 78 then 78 = 3 + (n-1)5 = n = 16.
Q5. Find the number of term in each of the following APs:
- 7 , 13 , 19 , ………, 205
- 18 , 31/2 , 13 , ………, -47
Solution:-
- 205 = 7 + (n-1)6
= 198 = (n-1)6
= n = 34
- -47 = 18 + (n-1)(-5/2)
= -65 = (n-1) (-5/2)
= n = 27.
Q6. Check whether -150 is a term of the AP: 11 , 8 , 5 , 2,…… .
Solution:-
-161 = -3n + 3 = 3n = 164
N = 54.67
Q7. Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Solution:-
A + 10d = 38
A + 15d = 73
A = -32 d = 7
A31 = -32 + 30 x 7
= -32 + 210
= 178
Q8. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 28th term.
Solution:-
A + 2d = 12
A + 49d = 106
A =8 d = 2
A29 = 8 + (29 – 1) x 2
8 + 56 = 64
Q9. If the 3rd and the 9th terms of an AP are 4 and -8 respectively, which term of this AP is zero ?
Solution:-
A + 2d = 4
A + 8d = -8
A = 8 d = -2
An = 0
8 + (n-1)(-2) = 0
N = 5
Q10. The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Solution:-
A17 = a10 + 7 = a + 16d = a + 9d + 7 = d = 1
Q11. Which term of the AP: 3 , 15 , 27 , 39 , …… will be 132 more than its 54th term?
Solution:-
A = 3 d = 12
An = a54 + 132
3 + ( n – 1)12 = 3 + (54 – 1)12 + 132
(n-1)12 = 768
N – 1= 64
N = 65
Q12. Two APs have the same common difference The difference between their 100th term is 100 , what is the difference between their 1000th terms ?
Solution:-
A100 – a`1000 = 100 = (a1 + 99d) – (a`1 + 99d ) = 100
A1 – a`1 = 100
A1000 – a`1000 = (a1 + 999d) – (a11 + 999d)
= a1 – a`1 = 100….
Q13. How many three digit numbers are divisible by 7 ?
Solution:-
Three digits numbers divisible by 7 are 105 , 112 , ….. 994.
Let the required number of numbers be n
994 = 105 + (n-1)7 = 7n = 896 = n = 128.
Q14. How many multiplies of 4 lie between 10 and 250 ?
Solution:-
A = 12 , d = 4 let an = 248
248 = 12 + (n-1)4 = (n-1)4 = 236
N – 1 = 59 = n = 1 + 59 = 60
Q15. For what value of n , are the nth terms of two AP : 63 , 65 , 67 , ….. and 3 , 10 , 17 , …. equal ?
Solution:-
63 + (n-1)2 = 3 + (n-1)7
60 = 5(n-1)
N = 13
Q16. Determine the AP whose third term is 16 and 7th term exceeds the 5th term by 12 ?
Solution:-
A3 = 16 and a7 = a5 + 12
A + 2d = 16 and a + 6d = a + 4d + 12
D = 6 and a= 4
Q17. The sum of the 4th and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first term three terms of an AP.
Solution:-
3 , 8 , 13, ……,253.
20th term from the end = 253 + (20 – 1)(-5)
= 158.
Q18. The sum of the 4th and 8th term of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms of an AP.
Solution:-
(a+3d) + (a+7d) = 24 = 2a + 10d = 24
A = 5d = 12 (I)
(a+5d) +(a+9d) = 44 = 2a + 14d = 44
A + 7d = 22 (ii)
Solving (I) and (ii)
A = -13 d = 5
This first three term are -13 , -8 and -3.
Q19. Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year In which year did his income reach Rs 7000 ?
Solution:-
An = 7000 Then 7000 = 5000 + (n-1)200
2000 = (n-1) 200 = n = 11.
Q20. Ramkali saved Rs 5 in the first week of a year and then increased her weekly savings by Rs 1.75 If in nth week , hr weekly savings become Rs 20.75 find n.
Solution:-
An = 20.75 20.75 = 5 + (n-1)(1.75)
N = 10