Question

If 7th term and 11th term of an AP are 37 and 57 respectively find first term and common difference. Also find 27th term .​

Answer 1

Answer:

d=5

27th term= 137

Step-by-step explanation:

l=a+ (n-1)d

where, l is the last term, a is the first term, n is the no. of terms and d is the common difference

according to question:

37= a+ (7-1)d______(1)

57= a+ (11-1)d______(2)

(2)-(1)=

20= 4d

d=5

and by putting the value of d in either of the equations,we get:

a=7

now;

l = 7+(27-1)5

l= 137

Answer 2

Question:-

If 7th term and 11th term of an AP are 37 and 57 respectively find first term and common difference. Also find 27th term.

Solution:-

Given,

• 7th term is 37 and 11th term is 57.

a 7 = a + 6d = 37 ........ ( 1 )

a 11 = a + 10d = 57 ........ ( 2 )

where a is first term and d is common difference.

( 2 ) - ( 1 )

a 11 => a + 10d = 57 ........ ( 2 )

a 7 => -a ± 6d = -37 ........ ( 1 )

➣ 4d = 20

➣ d = 20/4

➣ $\boxed{ \: d \: = \: 5 \: }$

Now,

Substitute d in equation ( 1 ) to get the first term:-

➣ a + 10d = 57

➣ a + 10(5) = 57

➣ a + 50 = 57

➣ a = 57 - 50

➣ $\boxed{ \: a \: = \: 7 \: }$

Now,

We have to find 27th term:-

➣ a = 7 ; d = 5 ; t 27 = ?

➣ tn = a + ( n - 1 ) d

➣ t 27 = 7 + (27 - 1)5

➣ t 27 = 7 + 26(5)

➣ t 27 = 7 + 130

➣ $\boxed{ \: t 27 \: = \: 137 \: }$

Verification:-

➣ a + 10d = 57

➣ 7 + 10(5) = 57

➣ 7 + 50 = 57

➣ $\boxed{ \: 57 \: = \: 57 \: }$