Question

1) If the nth and 13th terms of an AP are 34 and 64
respectively. then its 18th term is .......​

Answer 1

Answer:

18th term is 89.

Step-by-step explanation:

It is given that 7th & 13th terms are 34 & 64.

t7 = 34

t13 = 64

tn = a + (n - 1) * d

=> 34 = a + (7 - 1) * d

=> 34 = a + 6d .... (1)

Now

t13 = a + (13 - 1) * d

=> 64 = a + 12 * d

=> 64 = a + 12d ......(2)

Subtract eqn (1) from eqn (2)

a + 12d = 64

a + 6d = 34

=> 0 + 6d = 30

=> 6d = 30

=> d = 30/6

=> d = 5

Put d = 5 in (1)

a + 6d = 34

=> a + 6 * 5 = 34

=> a + 30 = 34

=> a = 34 - 30

=> a = 4

Now,

tn = a + (n - 1) * d

=> t18 = 4 + (18 - 1) * 5

=> t18 = 4 + 17 * 5

=> t18 = 4 + 85

=> t18 = 89

Hence,

18th term is 89.