find the 31st term of AP whose 11th term is 38 and 16th term is 73
Answers
Answer:
178
Step by step explanations:
Given that,
In an AP,
11th term is 38
so,
a + (11 - 1)d = 38
a + 10d = 38. ......(1)
also,
16th term is 73
a + (16 - 1)d = 73
a + 15d = 73.....(2)
now,
(2) - (1)
5d = 35
d = 35/5
d = 7
now,
outting the value of d in (1)
a + 10(7) = 38
a + 70 = 38
a = 38 - 70
a = -32
d = 7
so,
31st term of the AP
a + (31 - 1)d
-32 + 30(7)
-32 + 210
178
so,
31st term of the AP = 178
Answer:
178.
Step-by-step explanation:
Given,
11th term of the AP is 38
16th term of the AP is 73
From the properties of AP :
- nth term = a + ( n - 1 )d { where a is the first term and d is the common difference between the terms }
Let the first term of this AP be a and common difference between the terms be d.
⇒ 11th term = a + ( 11 - 1 )d
⇒ 38 = a + 10d ...( 1 )
⇒ 16th term = a + ( 16 - 1 )d
⇒ 73 = a + 15d ...( 2 )
Subtracting ( 2 ) from ( 1 ) :
⇒ a + 10d - ( a + 15d ) = 38 - 73
⇒ a + 10d - a - 15d = - 35
⇒ - 5d = - 35
⇒ d = 7
Hence,
⇒ 38 = a + 10d
⇒ 38 = a + 10( 7 )
⇒ 38 = a + 70
⇒ 38 - 70 = a
⇒ - 32 = a
Therefore,
⇒ 31st term = a + ( 31 - 1 )d
= - 32 + 30( 7 )
= - 32 + 210
= 178
Hence 31st term of the AP is 178.