Question

The 11 term and the 21 term of an AP 16 and 29 respectively then find The 1 term and common difference The 34 term 'n' such that tn = 55

Answer 1

As given :-

a11 = 21

a + 10d = 21 .......... ( i )

and,

a16 = 29

a + 15d = 29 ....... ( ii )

Sub ( ii ) from ( i )

a + 10d - ( a + 15d ) = 21 - 29

a + 10d - a - 15d = -8

-5d = -8

d = -8/-5

d = 8/5

Putting value of d in equation ( i )

a + 10d = 21

a + 10×8/5 = 21

a + 16 = 21

a = 21 -16

a = 5

So, common difference = 8/5

and 1st term = 5

Now , n = 34

an = a + ( n - 1 )d

a34 = 5 + 33×8/5

a34 = 5 + 264/5

a34 = (25+264)/5

a34 = 289/5