Find the sum of first 30 terms of an A.P. whose second term is 2 and s

1.	Find the sum of first 30 terms of an A.P. whose second term is 2 and seventlhterm is 22.
Answer» Using formula of nth term an = a + (n-1) d Here, given that a2 = 2 => a+d = 2 ..............(1)&a7 = 22 => a+6d = 22.... .....(2) solving (1)&(2) we get(2-d) + 6d = 22=> 5d = 22-2= 20=> d = 4now put the value of d in (1) we get, a + 4= 2=> a= -2 Now, Using formula for sum of first n termsSn = n/2{2a + (n-1) d} The sum of first 30 terms of an A.P.= Here, n= 30= 30/2 {2×(-2) +(30-1)×4}= 15 {-4 +120 - 4}= 15 × 112= 1680 Hence, The sum of first 30 terms of an AP = 1680

Find the sum of first 30 terms of an A.P. whose second term is 2 and seventlhterm is 22.

Answer»

Using formula of nth term an = a + (n-1) d

Here, given that a2 = 2 => a+d = 2 ..............(1)&a7 = 22 => a+6d = 22.... .....(2)

solving (1)&(2) we get(2-d) + 6d = 22=> 5d = 22-2= 20=> d = 4now put the value of d in (1) we get, a + 4= 2=> a= -2

Now, Using formula for sum of first n termsSn = n/2{2a + (n-1) d}

The sum of first 30 terms of an A.P.= Here, n= 30= 30/2 {2×(-2) +(30-1)×4}= 15 {-4 +120 - 4}= 15 × 112= 1680

Hence, The sum of first 30 terms of an AP = 1680