# Find the value of k and 17th term of each of the following arithmetic sequences.

1
by DanV

2016-06-28T18:02:32+08:00
1. 5k -3 - (2k +1) = 7k -2 -(5k-3)
5k -3 -2k -1 = 7k -2 -5k +3
3k -4 = 2k +1
3k -2k = 1+4
k = 5

a₁ = 2k +1 = 2(5) +1 = 10+1 = 11
a₂ = 5k - 3 = 5(5) - 3 =  25-3 = 22
a₃ = 7k - 2 = 7(5) - 2 = 35 - 2 = 33
a₁₇ = a₁ + (n-1)d
a₁₇ = 11 + (17-1)11
a₁₇ = 11 + (16)11
a₁₇ = 11 + 176
a₁₇  = 187

2. 5k + 4 -(7k + 2) = 4k - 5 - (5k +4)
5k + 4 - 7k - 2 = 4k - 5 - 5k - 4
-2k + 2 = -k -9
2+9 = 2k -k
11 = k

a₁ = 7k +2 = 7(11) +2 = 77 +2 = 79
a₂ = 5k +4 = 5(11) +4 = 55 +4 = 59
a₃ = 4k -5 = 4(11) -5 = 44 -5 = 39
a₁₇ = a₁ + (n-1)d
a₁₇ = 79 + (17-1)20
a₁₇ = 79 + (16)20
a₁₇ = 79 + 320
a₁₇ = 399

3. 2k -5 - (3k +7) = 6k -2 - (2k -5)
2k -5 -3k -7 = 6k -2 -2k +5
-k -12 = 4k +3
-12 -3 = 4k +k
-15 = 5k
-3 = k

a₁ = 3k +7 = 3(-3) +7 = -9 +7 = -2
a₂ = 2k -5 = 2(-3) -5 = -6 -5 = -11
a₃ = 6k -2 = 6(-3) -2 = -18 -2 = -20
a₁₇ = a₁ + (n-1)d
a₁₇ = -2 + (17-1) -9
a₁₇ = -2 + (16) -9
a₁₇ = -2 -144
a₁₇ = -146