Question

Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.​

Answer 1

Answer:

31st term of the AP is 178

Step-by-step explanation:

$a_n =a_1 + (n - 1)d \\ a_n = the \: nᵗʰ \: term \: in \: the \: sequence \\ </p><p>a_1 = the \: first \: term \: in \: the \: sequence \\ </p><p>d = the \: common \: difference \: between \: terms$

Lets find out the first term and common difference

$a_n =a_1 + (n - 1)d \\ a_{11} =a_1 + (11 - 1)d \\ 38 =a_1 + 10d \: \: \: \: \: \: \: \: ...(1) \\ \\ a_{16} =a_1 + (16 - 1)d \\ 73 =a_1 + 15d \: \: \: \: \: \: \: ...(2)$

Solving (1) and (2)

$a_1 + 15d = 73 \\ a_1 + 10d = 38 \\ - - - - - - - \\ 5d = 35 \\ d = 7$

Common difference, d is 7

And first term is - 32

$a_1 + 15d = 73 \\ a_1 + 15 \times 7 = 73 \\ a_1 + 105 = 73 \\ a_1 = 73 - 105 = - 32$

Now let's fond out the 31st term

$a_{31} =a_1 + (31 - 1)d \\ a_{31} = - 32 + (31 - 1)7 \\ a_{31} = - 32 + 30 \times 7 \\ a_{31} = - 32 + 210 = 178$

31st term is 178