the 10th & 20th termof an AP are 73 & 143 find the 1st term the common difference & 30th term of AP

according to the question T_{10} = a = ( n- 1 ) d

73 = a+(10-1)d

73 = a + 9d .................... equation 1

now ..

T_{20}= 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 .......

**
**