Question

If the 3rd term and 9th term of an AP are 17 and 47 respectively, find:

(i) the common difference
(ii) the 20th term
(iii) the sum of the first six terms
A) (i) Common difference = 5, (ii) 83, (iii) 78
B) (i) Common difference = 6, (ii) 91, (iii) 94
C) (i) Common difference = 6, (ii) 83, (iii) 94
D) (i) Common difference = 5, (ii) 91, (iii) 78

Answer 1

The common difference is 30, the 20th term is 587, and the sum of the first six terms is 552.

Step-by-step explanation:

To find the common difference of an arithmetic progression (AP), we subtract the 3rd term from the 9th term:

47 - 17 = 30

So the common difference is 30.

To find the 20th term, we use the formula:

an = a + (n-1)d

where a is the first term, n is the position of the term, and d is the common difference. In this case, we have:

a = 17, n = 20, d = 30

a20 = 17 + (20 - 1) * 30

a20 = 17 + 19 * 30

a20 = 17 + 570

a20 = 587

So the 20th term is 587.

To find the sum of the first six terms, we use the formula:

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

where Sn is the sum of the first n terms. In this case, we have:

n = 6, a = 17, d = 30

S6 = 6/2 * (2 * 17 + (6-1) * 30)

S6 = 3 * (34 + 5 * 30)

S6 = 3 * (34 + 150)

S6 = 3 * 184

S6 = 552

So the sum of the first six terms is 552.