1Write the formula for finding the sum of the first n terms of an arithmetic series whose first and last terms are given.
2If the sum of the first 10 terms of an arithmetic series is 80 and the sum of the first 9 terms of the same series is 72, find the 10th term.
3What is the sum of the first 5 odd natural numbers?
4What is the sum of the first 5 even natural numbers?
5Find the sum of the series \( -37 - 33 - 29 - \cdots \) to 12 terms.
6Find the sum of the series \( 5 + 8 + 11 + 14 + \cdots \) to 20 terms.
7Find the sum of the series \( 7 + 10\frac{1}{2} + 14 + \cdots + 84 \).
8Find the sum of the series \( -5 + (-8) + (-11) + \cdots + (-230) \).
9Find the sum of the series \( \sum_{n=1}^{10}(2n+1) \).
10Find the sum of the series \( \sum_{n=2}^{15}(n+2) \).
11The first term and the common difference of an arithmetic series are 2 and 8 respectively. Find the sum of the first 10 terms.
12If the common difference and the sum of the first 9 terms of an AP are 5 and 75 respectively, find the first term.
13Find the common difference of an arithmetic series whose first term is 3 and the sum of the first 8 terms is 192.
14How many terms of the series \( 9 + 6 + 3 + \cdots \) must be taken so that the sum of the series is zero?
15Find the sum of all numbers from 50 to 150 which are exactly divisible by 9.
16Find the sum of all two-digit numbers which are multiples of 5.
17Find the sum of the odd numbers between 0 and 50.
18The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms.
19The first term of an AP is \( -9 \), the last term is 47 and the sum is 152. Find the number of terms.
20How many terms of the series \( 20 + 18 + 16 + \cdots \) must be taken so that the sum of the series may be 110? Explain the double answer.
21If the 3rd term and 11th term of an AP are 18 and 50 respectively, find (i) the first term and the common difference, (ii) the arithmetic series, (iii) the sum of the first 20 terms.
22If the 2nd term and 12th term of an AP are 20 and 50 respectively, find (i) the first term and the common difference, (ii) the sum of the first 25 terms.
23If the sum of the first 7 terms of an AP is 49 and that of 17 terms is 289, (i) find the first term and the common difference, (ii) find the arithmetic series, (iii) find the sum of the first 20 terms.
24The sum of three terms of an AP is 30 and their product is 840. Find the three terms.
25The sum of three terms of an AP is 12 and the sum of their squares is 56. Find the three terms.
26A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find (i) the first prize, (ii) the 2nd prize, (iii) the 3rd prize, (iv) the seventh prize.
27Four consecutive terms of an AP add up to 32 and the sum of their squares is 276. Find the four terms.
28Find the sum of the first 100 natural numbers.
29Why is the number of terms in \( 3 + 7 + 11 + \cdots + 43 \) not equal to \( \frac{43 - 3}{4} \)? Find the correct number of terms and the sum.
30The sum of the first 9 terms of an AP is 81. Find its 5th term without finding a or d.