# Arithmetic Progressions – Class X – Part 6 | Sum of first n terms (AP) | Exercise 5.3 | Q7-13 Solved

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

Arithmetic Progressions – Class X – Part 6 | Sum of first n terms (AP) | Exercise 5.3 | Q7-13 Solved

Topics discussed:

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 5.3 | Q7-13 Completely Solved with easy explanation

7. Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

8. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

9. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

10. Show that a1, a2, . . ., an, . . . form an AP where an is defined as below :
(i) an = 3 + 4n (ii) an = 9 – 5n
Also find the sum of the first 15 terms in each case.

11. If the sum of the first n terms of an AP is 4n – n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

12. Find the sum of the first 40 positive integers divisible by 6.

13. Find the sum of the first 15 multiples of 8.

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