Question

The 32th term of an Ap whose 11th term is 38 &16th term is 73​

Answer 1

Answer:

185

Step-by-step explanation:

a + 31d = 32th term = 185

d = 7 , a = -32

Answer 2

Answer:

185

Step-by-step explanation:

Given:

$T_{11} =38$

$T_{16} =73$

To solve: $T_{32}$

Solution:

$T_{11} = a+ (11-1)d$                          [$T_{n} =a + (n-1)d$ where 'a' is the first  term,

$38 = a+ (10)d$ ------(1)                                         'd' is the common difference ]  

similarly,

$73 = a+ (15)d$ --------(2)

solving (1) and (2) simultaneously we get the values to 'a' and 'd'

a= -32 and d= 7

Hence,

$T_{32}= a + (32-1)d$

$T_{32}= -32 + (31) 7$

$T_{32} = 185$