Question

The sixth term of an ap is 17 and tenth term is 33 find the first term and common difference

Answer 1

Answer:

first term                   =-3

common difference=4

Step-by-step explanation:

nth term of an AP=a+(n-1)d

a=first term

d=common difference

6th term=a+(6-1)d

a+5d=17(equation 1)

10th term=a+(10-1)d

a+9d=33(equation 2)

subtract equation 1 and 2

a+5d=17

a+9d=33

-   -    -

0-4d=-16

    d=4

substitute in equation 1

a+5(4)=17

a+20=17

a=17-20

a=-3

Answer 2

Answer:

first term= -3 , common difference=4

6th term=17

i.e 17=a+5d---(I)

similarly,

10th term=33

i.e 33=a+9d--(ii)

substract eq (ii) from (I)

we get,

a+9d=33

-(a+5d)=17

________

4d=16

d=4--(iii)

then put value of (d=4) in eq (I)

a+5(4)=17

a+20=17

a=-3