# Arithmetic Progression

Class 10 NCERT Exercise 5.2 Solution
1. #### Concept: nth term of AP

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 AP.

i. a = 7, d = 3 and n = 8 an = ?
ii. a = - 18, n = 10, an = 0, d = ?
iii. d = -3, n = 18, an = -5, a = ?
iv. a = -18.9, d = 2.5, an = 3.6, n = ?
v. a = 3.5, d = 0, n = 105, an = ?

2. #### Concept: nth term of AP

Choose the correct choice in the following and justify i. 30th term of the AP: 10, 7, 4, ....., is

1. 28
2. 77
3. -77
4. -87

ii. 11th term of the AP: -3, -$$frac{1}{2}$, 2, ....., is 1. 28 2. 22 3. -38 4. -48$\frac{1}{2}$ 3. #### Concept: Terms of Arithmetic Progression In the following APs, find the missing terms in the boxes: i. 2, $\square$, 26 ii. _________, 13, _________, 3 iii. 5, _________, _________, 9½ iv. -4, _________, _________, _________, _________, 6 v. _________, 38, _________, _________, _________, -22 4. #### Concept: Find 'n' in an AP Which term of the AP: 3, 8, 13, 18, ......, is 78? 5. #### Concept: Number of terms in AP Find the number of terms in each of the following APs: i. 7, 13, 19, ......, 205 ii. 18, 15½, 13, ......, -47 6. #### Concept: AP nth term formula Check whether -150 is a term of the AP: 11, 8, 5, 2 7. #### Concept: Find a, d, and nth term of AP Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73. 8. #### Concept: Find first term, common difference and nth term An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term. 9. #### Concept: Find n if nth term of an AP is zero If the 3rd and the 9th terms of an AP are 4 and -8 respectively, which term of this AP is zero? 10. #### Concept: Compute common difference of AP The 17th term of an AP exceeds its 10th term by 7. Find the common difference. 11. #### Concept: Find 'n' and 'd' of an AP Which term of the AP: 3, 15, 27, 39, … will be 132 more than its 54th term? 12. #### Concept: Difference between nth term of 2 APs with same common difference Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms? 13. #### Concept: AP with d = 7. Multiples of 7 How many three-digit numbers are divisible by 7? 14. #### Concept: AP with d = 4; multiples of 4 How many multiples of 4 lie between 10 and 250? 15. #### Concept: nth term of 2 APs is same For what value of n, are the nth terms of two APs: 63, 65, 67, …. and 3, 10, 17, ….. equal? 16. #### Concept: Find AP given some terms of the AP Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12. 17. #### Concept: Find$n - 19)th term of an AP

Find the 20th term from the last term of the AP: 3, 8, 13, ...... 253.

18. #### Concept: Find first term given sum of some terms of an AP

The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

19. #### Concept: Word Problem in Arithmetic Progression

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?

20. #### Concept: Word Problem in Arithmetic Progression

Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by R. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n.