fifth term of an A.P exceeds twice the 2nd term by 1 the 10th term exceeds twice the 4th term by 3 find common difference and first term
Answers
Given : The 5th term of an A.P. exceeds twice the 2nd term by 1. The 10th term exceeds twice the 4 th term by 3.
To Find : the first term and the common of the A.P.
Solution:
First term = a
Common difference = d
AP a , a + d , a + 2d , . . .
nth term = a + (n - 1) d
2nd term = a + d
5th term = a + 4d
a + 4d = 2(a + d) + 1
=> a + 4d = 2a + 2d + 1
=> 2d - a = 1
1oth term = a + 9d
4th term = a + 3d
a + 9d = 2(a + 3d) + 3
=> a + 9d = 2a + 6d + 3
=> 3d - a = 3
2d - a = 1
3d - a = 3
=> d = 2
a = 3
First term = 3
common difference = 2
AP
3 5 7 9 11 13 and so on
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