Question

Find the general term and 10th term for the sequence 9, 12, 15,18​

Answer 1

Solution:-

9, 12 , 15 , 18, ............................

=> a ( first term ) = 9

=> d ( common difference) = 12 - 9 = 3

Formula = Tn= a + ( n - 1 )d

=> Tn = 9 + ( n - 1 ) 3

=> Tn = 9 + 3n - 3

=> Tn = 3n + 6

Now we have find n= 10 th term

T10= 3 × 10 + 6

= 30 + 6

= 36

So 10th term of an AP = 36

Answer 2

Given ,

First term (a) = 9

Common difference (d) = 3

We know that ,

The general formula or nth term of an AP is given by

$\boxed{ \sf{ a_{n} = a + (n - 1)d }}$

Thus ,

$\sf \mapsto a_{n} = 9 + (n - 1)3 \\ \\ \sf \mapsto a_{n} =9 + 3n - 3 \\ \\ \sf \mapsto a_{n} =6 + 3n$

Therefore ,

• The general formula of given AP is 6 + 3n

Now , the tenth term of given AP will be

$\sf \mapsto a_{10} = 9 + (10 - 1)3 \\ \\ \sf \mapsto a_{10} =9 + 27 \\ \\ \sf \mapsto a_{10} =36$

Therefore ,

• The tenth term of given AP is 36