Find the second term and nth term of an A.P. whose 6th term is 12 and 8th term is 22.
Answers
Answer:
The second term is - 8 & nth term is -18 + 5n .
Step-by-step explanation:
Given :
a6 = 12 & a8 = 22
a6 = 12
a + (6 - 1)d = 12
[an = a + (n -1)d]
12 = a + 5d
a + 5d = 12 ……………(1)
a8 = 22
a + (8 - 1)d = 22
a + 7d = 22 ………..,..(2)
On Subtracting eq 1 from eq 2,
a + 7d - (a + 5d) = 22 - 12
a + 7d - a - 5d = 10
2d = 10
d = 10/2
d = 5 ……………..(3)
On putting the value of d = 5 in equation 1
a + 5d = 12
a + 5(5) = 12
a + 25 = 12
a = 12 - 25
a = -13 …………..(4)
2nd term :
a2 = a + (2 - 1)d
a2 = a + d
a2 = -13 + 5
[From eq 3 & 4]
a2 = -8
nth term :
an = a + (n -1)d
an = -13 + (n -1)5
[From eq 3 & 4]
an = - 13 + 5n - 5
an = - 13 - 5 + 5n
an = -18 + 5n
Hence, the second term is - 8 & nth term is -18 + 5n .
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GIVEN :
Sixth term of an A.P = 12
a + 5d = 12 ------(1)
Eighth term of an A.P = 22
a + 7d = 22 ----(2)
Solve eq - (1) & (2) to find difference (d)
a + 5d = 12
a + 7d = 22
(-)
-----------------
-2d = -10
d = 10/2
d = 5
Difference = 5
Substitute d in eq - (1) to find first term (a)
a + 5d = 12
a + 5(5) = 12
a + 25 = 12
a = 12 - 25
a = -13
First term = -13
Second term :
= a + d
= -13 + 5
= -8
an = a + ( n - 1 )d
= -13 + ( n - 1) 5
= -13 + 5n - 5
= -18 + 5n
= 5n - 18
Therefore, nth term of A.P is 5n - 18 and second term of A.P is -8.