# Arithmetic Progressions-Class X-Part 4 | nth term of an AP | Exercise 5.2-5.3 | Sum of n terms (AP)

### Watch the fourth video session on “Arithmetic Progressions” for Class Xth – concepts and solved questions.

Arithmetic Progressions-Class X-Part 4 | nth term of an AP | Exercise 5.2 Q16-20- Exercise 5.3 Q1 | Sum of n terms (AP)

Topics discussed:

nth term of an AP; Exercise 5.2 | Q16-20 Completely Solved with easy explanation

Sum of first n terms of an AP: Expression for some derived:

S = (n/2) [ 2a + (n-1)d ]
S = (n/2) [ first term + last term ] = (n/2) [ a + l ]

Where a = first term, d = common terms, n = number of terms of the given AP, S = Sum of first n terms, l = a+(n-1)d = last term.

Exercise 5.2 | Q16-20 Completely Solved with easy explanation

16. Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

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

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

Exercise 5.3 | Q1 Completely Solved with easy explanation

1. Find the sum of the following APs:

(i) 2, 7, 12, . . ., to 10 terms.
(ii) –37, –33, –29, . . ., to 12 terms.
(iii) 0.6, 1.7, 2.8, . . ., to 100 terms.
(iv) 1/15 , 1/12 , 1/10 , . . ., to 11 terms.

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