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# C2 Sequences =S watch

1. The sum of the first two terms of an arithmetic progression is 18 and the sum of the first four terms is 52. Find the suum of the first 8 terms.

The sum of the first twenty terms of an arithmetic progression is 50, and the sum of the next twenty terms is -50. Find the sum of the first hundred terms of the progression.

Find the sum of the arithmetic progression 1,4,7,10,13,16....,1000.
Every third term of the above progression is removed, i.e 7,16 etc. Find the sum of the remaining terms.

Can anyone tell me step by step how to work it out? Please?
2. Sum = (n/2)(2a+(n-1)d)

Sum of 2 terms 2a+d=18
so 4a+2d=36 (1)

Sum of 4 terms 2(2a+3d)=52
so 4a+6d=52 (2)

subtract (1) from(2)
gives 4d=16 so d=4
from(1) 4a+8=36
so a=7

sequence is 7, 11, 15, 19

Sum to 8 terms

4(14+7.4)=4.42=168

Try the next one.
3. The sum of the first twenty terms of an arithmetic progression is 50, and the sum of the next twenty terms is -50. Find the sum of the first hundred terms of the progression.

Sum to 20 terms: 10(2a+19d)=50
20a+190d=50
40a+380d=100 (1)

Sum to 40 terms: 20(2a+39d) = 0
40a+780d =0 (2)

(2)-(1) 400d = -100
d=-0.25

from (1) 40a-95=100
40a=195
a=4.875

sum to 100 terms: 50(9.75 +99(-0.25))
=-750

Try the last one?

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