Question

The first term of an arithmetic sequence is 7 and the sixth term is 22. Find
(a) The common difference;
(b) The twelfth term;
(c) The sum of the first 100 terms.

Answer 1

Answer:

(a) 3

(b) 40

(c) 15,550

Step-by-step explanation:

(a) Given a = 7

term-6 i.e. a+5d=22

put a=7 in a+5d

i.e. a+7d=22

7+5d=22

5d=15

d=3.

(b) term - 12 = a+11d

i.e. 7+11(3)

= 7+33

=40.

(c) S sub 100 = 100/2 [2(7)+ {100-1}3]

= 50 [14+{99(3)}

=50 {14+297}

=50 {311}

=15,550