Question

Algebraic form of an arithmetic sequence is 6n + 2
(a) What is its first term.
(b) What is the 25th term.
(c) What is the sum of first 25 terms of this sequence.​

Answer 1

Answer:

a) n=1

6n+2 = 6*1+2=6+2=8

1st term =8

b) x25= x1 + common difference

Common difference =

n=2

6 *2+2= 14.

common difference = x2-x1

=14-8=6

x25=x1+24*6

8+24*6

8+144=152

b) 25th term = 152

c) S25= n/2 ( x1+xn)

25/2(8+152)

25/2*160

25*80=2000

Hope this help

Answer 2

Solution :

♪ For any arithmetic sequence, the first term has n = 1

Hence, first term is 6(1) + 2 = 8

b) What is the 25th term.

Solution → put n = 25

6 ( 25 ) + 2 = 150 + 2 = 152

c) what is the sum of first 25 terms of these sequence.

Solution → By using formula Sn = n / 2 ( a1 + an )

given, Sn = sum of n terms

n = number of terms

a1 = first term

Sn = n / 2 ( a1 + an )

$s25 = \frac{25}{2} (8 + 152) \\ = \frac{25}{2} (160) \\ 2000$