Question

What is the 21st term of the arithmetic sequence 3,5,7,9......?​

Answer 1

Answer:

120

Step-by-step explanation:

the sum of n terms of arithmetic sequence is

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

where a is the first term and d the common difference

here a = 3 d=7-5=5-3=2, n=10

S10=5((2×3)+(2×9))

=5(6+18)=120

Answer 2

The 21st term of given arithmetic sequence is 43.

We have to find the 21st term of the arithmetic sequence of 3 , 5 , 7 , 9 ....

Arithmetic sequence :

• It is the sequence in which the difference between one term and its next term is constant.
• If first term is a and common difference is d, then arithmetic sequence is represented by; a , a + d, a + 2d , a + 3d, a + 4d, .... a + (n - 1)d.
• nth term of an arithmetic sequence is given by, aₙ = a + (n - 1)d

Here sequence is ; 3 , 5 , 7 , 9 ....

First term, a = 3

Common difference , d = 5 - 3 = 7 - 5 = 2

Use formula, nth term, aₙ = a + (n - 1)d

⇒ 21st term , a₂₁ = 3 + (21 - 1) × 2

= 3 + 20 × 2

= 43

Therefore the 21st term of given arithmetic sequence is 43.

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