Question

The 6th and the 17th terms of an AP are 21 and 54 respectively . The first term of the AP is _?​

Answer 1

Answer:

a6 = 21

a17 = 54

an = a +(n-1) d

a6 = a +(6 - 1) d

21 = a+ 5d............ (i)

a17 = a + ( 17 - 1)d

54 = a + 16d....(ii)

by substitution method,

21 - 5d = a.........(iii)

substitute iii in ii

54 = 21 - 5d + 16d

54 - 21 = 11d

33 = 11d

d = 3

substitute d in i

21 = a + 5d

21 = a + 5*3

21 - 15 = a

a=6

therefore the first term of the ap is 6

AP : 6,9,12,15.......

hope it helps you...

Answer 2

Answer:

$given - > \\ \\ a + 16d = 54 \\ a + 5d = 21 \\ subtracting \: \: {eq}^{n} 2\: \: from \\ {eq}^{n} 1\: \: we \: \: have \\ \\ 11d = 33 \\ = > d = 3$

..

..

For 6th term ,

a + 5d = 21

=> a= 21 - 5×3

=> a = 6

..

Therefore, the 1st term of the AP is 6 .