Question

The seventh term of an arithmetic sequence is 40 and its 13th term in is 82
a. what is its common difference
b. what is its 19th and 10th term

Answer 1

Given

7th term of an ap is 40 and 13 th term is 82

To Find

a. what is its common difference

b. what is its 19th and 10th term

$\sf\huge {\underline{\underline{{Solution}}}}$

Formula for finding 'nth term ':

an= a+(n-1)d

7th term can also be written as : a+(7-1)d

=> a+6d

=>a+6d=40-----(1)

13th term can also be written as: a+(13-1)d

=> a+12d

=> a+12d= 82----(2)

substracting Equation 1 from Equation 2

=> a+12d -(a+6d)= 82-40

=> a+12d-a-6d= 42

=> 6d= 42

=> d= 42÷6= 7

a.common difference is 7

Now, finding a

from equation 1

=> a+6d=40

=> a+42=40

=>a= 2

19th term can also be written as: a+18d

19th term => 2+18(7)= 2+126=128

10th term => a+9d = 2+9(7)= 63+2= 65

b. 19th term is 128

10th term is 65

Answer 2

Answer:

a)7

b)124 and 61

Step-by-step explanation:

let 'a' be first term and 'd' be common difference

according to question

T7=40

a+(7-1)d=40

 a+6d=40   ..(1)

and

T13=82

a+(13-1)d=82

a+12d=82  ..(2)

after subtracting (1) from (2)

we get 6d=42

then d=7     .. .. .. .. .. put this in (1)

a+6*7=40

a=-2

Then T19=a+(19-1)d

T19=-2+18*7=124

And

T10=a+(10-1)d

T10=-2+9*7=61