Question

The 10th term from the end of the ap 7,10,13....154;157 is?

Answer 1

The 10th term from the end of the AP is 39 th term

`\therefore a_(39) =114`

Explanation:

Given:

Arithmetic Sequence as

7 , 10 , 13........154,157

∴ First term = a₁ = 7

Second term = a₂ = 10

∴ Common Difference = d = a₂ - a₁ = 10 - 7 = 3

∴ d = 3

`a_(n) = 157`

To Find:

`a_(10) = ?`

Solution:

An equation for the nth term of the arithmetic sequence is given by

`a_(n) =a_(1) + (n-1)* d`

Substituting a₁ and d and we get

`157=7+(n-1)* 3\\150=3n-3\\\\3n=147\\n=(147)/(3)\\\\n=49\\`

There are 49 terms in given AP

Therefore the 10th term from the end will be 39th term

`a_(39) =a_(1) + (39-1)* 3=7+38* 3=114`

`\therefore a_(39) =114`