Question

Show that each of the progression given below is an AP. Find the first term, common difference and next term of each: (I) 9,15,21,27 (ii) 11,6,1,-4 (iii) -1,-5/ 6,-2/3,-1/2 (iv) root2 root8, root18,root32 (v) root20, root45, root80, root125

Answer 1

Answer:1

9,15,21,27

d=15-9

=6

a=9

a⁵=a+4d

=9+4(6)

=9+24

33

Step-by-step explanation:

Answer 2

Step-by-step explanation:

1. first term (a) = 9

common difference (d) = a2-a1

=15- 9 = 6

Next term,a5 = a +4d

=9+4×6 =33

2. a=11

d= 6-11 =-5

a5 = a+4d

=11+ 4×(-5) = -9

3. a=-1

d=-5/6+1 =1/6

a5 = a +4d

= -1+4×1/6 =-1/3

4.a=√2

d=√8-√2

=2√2-√2

=√2

a5 = a+4d

=√2+4×√2

=5√2

5. a= √20=2√5

d=√45-√20

=3√5-2√5

=√5

a5 =a+4d

=2√5+4√5

=6√5