Question

consider the arithmetic sequence 13,23,33.....
a. What is the algebraic expression for this sequence?
b. Find the 100 th term of this sequence?
c. Find the sum of first 20 terms of this sequence.​

Answer 1

Answer:

a. 10n+3

b. 1006

c. 2160

a. Let the first term be a

and common difference be d

From the A.P

a=13 and d=23-13=10

So nth term=a+(n-1)d=13+(n-1)10=13+10n-10

=10n+3

Algebraic expressions for this sequence

=10n+3

b.Number of terms(n)=100

Putting the value of n in the expression obtained

10n+3=10×100+3=1000+3=1003

c.Number of terms(n)=20

So sum of first 20 terms(S20)

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

=20/2[2×13+(20-1)10]

=10(26+19×10)

=10(26+190)

=10×216

=2160

Answer 2

a = 13 , d=23-13 = 10

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

= 13 + (n-1)10

= 13 +10n -10

= 3+10n

2) n= 100

An = a+(n-1)d

= 13 + (100-1)10

= 13 +99×10

= 990+13

= 1003

3) n= 20

Sn= n/2 { 2a +(n-1) d }

= 20/2 {26 + 19×10}

= 10×(26+190)

= 10 × 216

= 2160