Question

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

Answer 1

Answer:

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

$\therefore a_{39} =114$

Step-by-step 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

$a_{n} =a_{1} + (n-1)\times d$

Substituting  a₁  and d  and we get

$157=7+(n-1)\times 3\\150=3n-3\\\\3n=147\\n=\frac{147}{3}\\\\n=49$

There are 49 terms in given AP

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

$a_{39} =a_{1} + (39-1)\times 3=7+38\times 3=114$

$\therefore a_{39} =114$