# Arithmetic Progressions – Class X – Part 5 | Sum of first n terms (AP) | Exercise 5.3 | Q2-6 Solved

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Arithmetic Progressions – Class X – Part 5 | Sum of first n terms (AP) | Exercise 5.3 | Q2-6 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 | Q2-6 Completely Solved with easy explanation

2. Find the sums given below :

(i) 7 +10(1/2) + 14 + . . . + 84
(ii) 34 + 32 + 30 + . . . + 10
(iii) –5 + (–8) + (–11) + . . . + (–230)

3. In an AP:

(i) given a = 5, d = 3, an = 50, find n and Sn.
(ii) given a = 7, a13 = 35, find d and S13.
(iii) given a12 = 37, d = 3, find a and S12.
(iv) given a3 = 15, S10 = 125, find d and a10.
(v) given d = 5, S9 = 75, find a and a9.
(vi) given a = 2, d = 8, Sn = 90, find n and an.
(vii) given a = 8, an = 62, Sn = 210, find n and d.
(viii) given an = 4, d = 2, Sn = –14, find n and a.
(ix) given a = 3, n = 8, S = 192, find d.
(x) given l = 28, S = 144, and there are total 9 terms. Find a.

4. How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?

5. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

6. The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

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