Deriving the formula of Sn of A.P. (SP5.3)

Find the sum of –20, –15, –10, …, 100.

• 1000

• 2000

• 1200

• 10000

Given that an arithmetic progression 4, 10, 16, …, find the sum of the first 25 terms.

(a)  

Given that an arithmetic progression 4, 10, 16, …, find the sum of the first nth terms.

• 6n²+n

• 12n²+2n

• 3n²+n

• 2n²+n

Calculate the value of n of an arithmetic progression as such that the first term is –15, the common difference is –3 and the sum of the first n terms is –1 023.

(a)  

Calculate the sum of 200 terms after the first 50 terms of an arithmetic progression in which the sum of the first n terms is  $S_n=\frac{n}{2}\left(n+1\right)$  .

(a)  

Find the first term of the arithmetic progression in which the sum of the first 42 terms is 5 838 and the last term is -22.

• 300

• 20

• 3000

• 200

The diagram on the right shows the pattern drawn on a Cartesian plane. The final line on the plan is parallel to the y-axis and passes through x = –9. Find the sum of the length of the overall pattern.

(a)  

A swarm of bees started to make a new beehive. 3 hexagonal holes were made on the first day. 7 hexagonal holes were made on the second day and 11 hexagonal holes were made on the third day and followed on until the beehive is ready. Calculate the minimum number of days if there are more than 1 000 hexagonal holes made.

(a)