Question

12th term of an AP is 14 more than it’s 5th term and sum of these 2 terms is 36 find its first term and common difference

Answer 1

Step-by-step explanation:

5th term=a+(n-1)d=a+4d

12th term=14+5th term

a+11d=14+a+4d

7d=14

d=2

5th term+12th term =36

a+4d+14+a+4d=36

2a+8d=36-14

2(a+4d)=22

a+4d=11

a+8=11

a=3

so 1st term=a=3

common difference=d=2

Answer 2

1st term=a=3

Common difference=d=2

Step-by-step explanation:

Formula of nth term = $a_n=a+(n-1)d$

Where a = first term

$a_n$=nth term

d= common difference

n = No. of term

Substitute n = 5

5th term=$a+(n-1)d=a+(5-1)d=a+4d$

Substitute n = 12

12 th term = $a+(12-1)d=a+11d$

We are given that 12th term of an AP is 14 more than it’s 5th term

So,$a+11d=14+a+4d$

$7d=14$

$d=2$

We are given that sum of these 2 terms is 36

$a+4d+14+a+4d=36$

$2a+8d=36-14$

$2(a+4d)=22$

$a+4d=11$

$a+8=11$

$a=3$

1st term=a=3

Common difference=d=2

#Learn more:

5th term of AP is 21 and 11th term is 39 find first term, common difference and sum of first 5th term of series

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