Question

Find the first term of ap if 8th and 12th term are 39 & 59?

Answer 1

Answer:

d=4

a=11

Step-by-step explanation:

8=39

12=59

tn=a+n-1*d

39=a+8-1 *d

39=a+7d (1)

tn=a+(n-1)d

59=a+(12-1)d

59=a+11d (2)

subtract equations 1 and 2

59=a+7d

39=a+11d

- - -

20=4d

20=d

_

4

5=d

substituting d=5 in equations 1

39=a+7d

39=a+7*5

39 =a+35

39-35=a

4=a

Answer 2

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GIVEN :

The 8th term of an AP is 39 .

The 12th term of an AP is 59.

TO FIND :

The AP

ANSWER :

The general term,tn =

$tn = a + (n - 1)d$

where n is the nth term.

a is the first term.

d is the common difference.

t8 = a + ( 8 - 1) d

a + 7d = 39 ________(1)

t12 = a + (12 - 1) d

a + 11d = 59 _________(2)

Subtract (1) & (2) ,

(2) => a + 11d = 59

(1) => a + 7d = 39

(-) (-) (-)

_________________

4d = 20

d = 20/4

d = 5 .

Substitute the value of d = 5 in equation (1),,,,

(1) => a + 7 (5) = 39

a + 35 = 39

a = 39 - 35

a = 4

The first term of an AP is 4 .

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