Find the A.P. whose 7th and 13th terms are respectively 34 and 64

Explanation

Let a be the first term and d be the common difference of the A.P.
then `a_(n) = a + (n - 1) d`
Given `a_(1) = 34 " " therefore a + 6d = 34 ` …(i)
`a_(13) = 64 " "therefore a + 12d = 64 ` …(ii)
Subtracting (i) from (ii) , we get
`therefore 6d = 30`
`rArr d = 5 `
Putting d = 5 in (i), we get
` a + 30 = 34 `
a = 4
Thus a = 4 . d = 5
Hence , the required A.P. is
4, 9, 14 , 19 , 24 ,...