the sum of 7th and 8th term of an ap is 4 x + 7 and 11 term is 2 x + 5 find the five terms and the common difference for x equal to 1.
please it's emergency give answer
Answers
It has given that, sum of 7th and 8th term of an ap is 4x + 7 and 11th term is 2x + 5.
To find : find the five terms and the common difference for x = 1.
solution : we know, nth term of an ap is given by, Tn = a + (n - 1)d
so, 7th term = a + (7 - 1)d = a + 6d
8th term = a + (8 - 1)d = a + 7d
11th term = a + (11 - 1)d = a + 10d
a/c to question,
7th term + 8th term = 4x + 7
⇒a + 6d + a + 7d = 4x + 7
⇒2a + 13d = 4x + 7 ..............(1)
again, 11th term = 2x + 5
⇒a + 10d = 2x + 5 .........(2)
from equation (1) and (2),
(2a + 13d) - 2(a + 10d) = (4x + 7) - 2(2x + 5)
⇒-7d = 7 - 10
⇒d = 3/7
a = 2x + 5 - 10d = 2x + 5 - 30/7 = 2x + 5/7
for x = 1, a = 2 + 5/7 = 19/7
now 1st term = a = 19/7
2nd term = a + d = 19/7 + 3/7 = 22/7
3rd term = a + 2d = 19/7 + 6/7 = 25/7
4th term = a + 3d = 19/7 + 9/7 = 28/7
5th term = a + 4d = 19/7 + 12/7 = 31/7
Therefore 19/7, 22/7, 25/7, 28/7, and 31/7 are first five terms in the ap and common difference is 3/7.