Question

the 16 term of an A.P is 30 and it's 31 th term is 60,find the first term and common difference​

Answer 1

Given:

16th term of A.P is 30 and 31st term is 60.

To Find:

The first-term and common difference?

Step-by-step explanation:

• We have 16th term is 30 and 31st term is 60 we can write it as

                                  [tex]a_1_6=30\\ and\\ a_3_1=60[/tex]

• On comparing above equation with $a_n=a+(n-1)d$ we can write them as

                              [tex]a+15d=30\\ and\\ a+30d=60[/tex]

• Now solve both equation by substitution method

                         [tex]a=30-15d\\ \textrm{put the value in other equation}\\ 30-15d+30d=60\\ 15d=30\\ d=2\\ thus, a=0[/tex]

Hence first term is 0 and common difference is 2.