Question

find the sum of the first 21 term of the a.p. whose 2nd term is 8 and 4th term is 14

Answer 1

It is given that , a2= 8 and a4= 14
Now , We know that an= a + (n-1)d
So Applying this formula we get,
a2= a + (2-1)d
a + d = 8 ... .. . . . . . .(1)
a4= a + (4-1)d
a + (4-1)d = 14
a + 3d = 14 .. . . .. ... .. (2)
Soving these eqn we will get a , d .
So ,We now we Have : a =5 d= 3 n= 21
Now, Sn = n/2 (2a + (n-1)d )
S21= 21 / 2 (2 * 5 + (21-1)3
= 21/ 2 (10+ 20*3)
= 21 / 2 (10+60)
= 21 / 2 (70) 35
S21= 21 * 35
S21= 735