Question

If the 3rd term and 9th term of an AP are 17 and 47 respectively, find:
(i) the common difference
(ii) the 20th term
(iii) the sum of the first six terms​

Answer 1

Answer:

term of AP is given by a+(n-1)d

Step-by-step explanation:

3rd term is a+2d=17  (1)

9th term is a+8d=47   (2)

solve 1 and 2

a=5     d=6

i) d=6

ii) a+19d=5+19(6)

            =99

Answer 2

Answer:

d=5

20th term=102

sum=117

Step-by-step explanation:

a+2d=17

a+8d=47

-6d=-30

(i)d=5

a=7

(ii)20th term=a+(n-1)d

                  =a+19d

                  =7+19x5

                  =7+95

                  =102

(iii) the sum 0f the first six numbers

n=6

sum=n/2(2a+(n-1)d)

         = 6/2(2x7+5x5)

         =3(14+25)

         =3x39

         =117

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