Question

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

Answer 1

Answer:

Step-by-step explanation:

a+15d=73. Eq -1

a+10d=38. Eq-2

d=7

Substitute value of D in equation

a+10*7=38

a,=32

a+30d=x

X=242

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★11th term = 38

${\boxed{\sf\:{(a+10d)=38.....(1)}}}$

★Also

★16th term = 73

${\boxed{\sf\:{(a+15d)=73.....(2)}}}$

★Now

★Subtracting Equation (1) from (2) we get :-

5d = 35

${\boxed{\sf\:{d=\dfrac{35}{5}}}}$

d = 7

★Now here substitute the value of d in equation (1)

a + 10 × 7 = 38

a + 70 = 38

a = 38 - 70

a = - 32

${\boxed{\sf\:{Now\;31st\;term:-}}}$

a31 = a + 30d

= (-32) + 30 × (7)

= (-32) + 210

= 178

$\fbox{Here we get 31st term of AP is 178}$