1The incentive is Rs. 800 in Baisakh, Rs. 1000 in Jestha, and so on up to Rs. 2000 in Kartik. By how much does it increase every month?
2What is the total incentive received from Baisakh to Kartik 2079 BS?
3If the same rate of growth continues, what will the incentive be in Baisakh 2080 BS?
4What will be the total incentive the employee receives up to Baisakh 2080 BS?
5Find the sum: \( 7 + 11 + 15 + 19 + \dots \) to 20 terms.
6Find the sum: \( 4 - 1 - 6 - 11 - 16 - \dots \) to 7 terms.
7Find the sum: \( \frac{1}{2} + \frac{3}{2} + \frac{5}{2} + \dots \) to 16 terms.
8Find the sum: \( 5 + 10 + 15 + \dots + 65 \)
9Find the sum: \( -64 - 48 - 32 - \dots + 32 \)
10Find the sum of the first 10 odd numbers.
11Find the sum of the first 100 natural numbers.
12Find the sum of the natural numbers from 50 to 100.
13First term = 1, last term = 50 and sum of all terms = 204. Find the common difference.
14First term = 160, last term = 20 and sum of all terms = 440. Find the common difference.
15First term = 17, last term = \( -\frac{99}{8} \) and sum of all terms = \( \frac{407}{16} \). Find the common difference.
16Common difference = \( -3 \), number of terms = 10 and sum of all terms = 325. Find the first term.
17Common difference = 9, number of terms = 9 and sum of all terms = 108. Find the first term.
18Common difference = 3, number of terms = 10 and sum of all terms = 155. Find the first term.
19How many terms of the series \( 4 + 10 + 16 + 22 + \dots \) have a sum of 374?
20The first term of an arithmetic series is 36 and its common difference is 9. How many terms will have a sum of 540?
21Find the sum of the first 16 terms of an arithmetic series if its third term is \( -15 \) and its eighth term is 10.
22Find the sum of the first 20 terms of an arithmetic series if its fifth term is 10 and its eleventh term is 22.
23The sum of the first 6 terms of an arithmetic series is 75 and the sum of its first 12 terms is 390. Find the sum of the first 20 terms.
24The sum of the first 7 terms of an arithmetic series is 21 and the sum of its first 12 terms is 126. Find the series.
25A worker in a garment factory made 1000 Nepali caps (Dhaka Topi) in the first year and increased production by 100 every year. Can he make 15,000 caps in 10 years?
26A person starts a new job on a monthly salary of Rs. 60,000, and it increases by Rs. 24,000 every year. In how many years will he earn a total of Rs. 1 crore? (Interest is not included.)
27Why does every pair have the same total when an arithmetic series is written forwards and backwards?
28Use \( S_n = \frac{n}{2}(a + t_n) \) to show that \( 1 + 2 + 3 + \dots + n = \frac{n(n + 1)}{2} \), and use it to add the numbers from 1 to 50.