The 7th term of an A.P. is 32 and its 13th term is 62. Find the A.P.
Advertisement Remove all ads
Solution
Here, let us take the first term of the A.P. as a and the common difference of the A.P as d
Now, as we know,
`a_n = a + (n -1 )d`
So for the 7th term (n = 7)
`a_7 = a + (7 - 1)d`
32 = a + 6d .......(1)
Also for 12th term (n = 13
`a_13 = a + (13 - 1)d`
62 = a + 12d ......(2)
Now on substracting (2) from (1) we get
62 - 32 = (a + 12d) - (a + 6d)
30 = a + 12d - a - 6d
30 = 6d
`d = 30/6`
d = 5
Substiting the value of d in (1) we get
32 = a + 6(5)
32 = a + 30
a = 32 - 30
a = 2
So, the first term is 2 and the common difference is 5.
There the A.P is 2, 7, 12, 27, ....
Concept: Arithmetic Progression
Is there an error in this question or solution?
APPEARS IN
Advertisement Remove all ads