Question

The common difference of two arithmetic sequence are equal. The difference between their first terms is 10. a) What is the difference between the second terms ? b) What is the difference between the nth terms ? c) What is the difference between the sums of first n terms ? ​

Answer 1

Step-by-step explanation:

d =d'

a -a'= 10

a). a2 = a + (2-1)d

= a + d

a'2 = a' + (2-1)d'

=a' + (1)d'

= a' + d

a2 - a'2 = a + d -a' - d

= a -a'

= 10

b). an= a + (n-1)d

= a + nd -d

a'n = a' + (n-1)d

= a' + nd -d

an-a'n = a+ nd -d - a' - nd +d

= a -a'

= 10

c) Sn = n/2 [2a + (n-1)d]

= n/2 ( 2a + nd -d)

= an + n^2d/2 -nd/2

S'n = n/2 [2a' + (n-1)d]

= n/2 (2a' + nd- d)

= a'n + n^2d/2 -nd/2

Sn -S'n = an + n^2d/2 -nd/2 -a'n - n^2d/2 + nd/2

= ( a -a')n

= 10n