the 10th & 20th termof an AP are 73 & 143 find the 1st term the common difference & 30th term of AP
according to the question T10 = a = ( n- 1 ) d
73 = a+(10-1)d
73 = a + 9d .................... equation 1
now ..
T20= a+(n-1)d
143 =a+ (20-1) d
143 = a + 19d ........... equation 2
equation 2 - equation 1
a+19d = 143
a+9d =73
=> 10d = 70
=> d = 7
substituting value of d in any equation you will get " a "
a=9d+73
a = 10.........
so the 30 th term is
a + (n-1)d
10+ (30-1)(7)
10 + 203
213 ......
so the first term is 10 , common difference is 7 and 30 th term is 213 .......