Find whether 55 is a term of the AP 7, 10, 13, … or not. If yes, find which term it is.

Explanation

Yes, let the first term, common difference and the number of terms of an AP are a,d and n respectively.
Let the `n`th term of an AP, be 55. i.e., `T_(n)=55`
We know that, the `n`th term of an AP, `T_(n)=a+(n-1)d " " …(i)`
Given that, first term (a) = 7 and common difference (d) `= 10 -7=3`
` "From Eq. (i), " 55=7+(n-1)xx3`
`implies 55=7+3n-3implies55=4+3n`
`implies3n=51`
` :. n=17`
Since, `n` is a positive integer. So, 55 is a term of the AP.
Now, put the values of a, d and n in Eq. (i),
`T_(n)=7+(17-1)(3)`
` " " =7+16xx3=7+48=55`
Hence, 17th term of an AP is 55.