questions (2 Viewers)

[Arithela]

1. The sum of the first 5 terms of an AP is 35 and the sum of the next 5 terms is 160. Find the first term and the common difference.

2. Prove that Tn = Sn - S(n-1) for any series.

3. The 20th term of an AP is 131 and the sum of the 6th to 10th term inclusive is 235. Find the sum of the first 20 terms.

 

[undalay]

1.

S₅ = 35 = 5/2(2a+4d)
14 = 2a + 4d ...1

S₁₀ = 35+160 = 195
195 = 10/2(2a+9d)
39 = 2a + 9d ...2

subtracting 1 from 2

25 = 5d
d = 5
Sub d=5 into (1)

14 = 2a + 20
2a = -6
a = -3

Thus, a = -3, d = 5

2.

S_n-1 = T₁ + T₂ + ... + T_n-1 ...(1)
S_n = T₁ + T₂ + ... + T_n-1 + T_n ...(2)
Subtracting (1) from (2)...

S_n - S_n-1 = T_n


3.
Same kind of method as 1. Just combine the equations and simultaneous.