Question

10th term of an arithmetic sequence is 34 and 20th term is 64 What is the remainder when the terms are divided by its common difference ?​

Answer 1

Answer:

The remainder is 1

Explanation:

We know,

→ nth term of an A.P. = a + (n - 1)d

Where,

• a denotes the first term
• n denotes the number of terms.
• d is the common difference.

For the first case :-

Where 10th term is 34.

Then,

→ 34 = a + (10 - 1)d

→ 34 = a + 9d. . . . . (i)

And also, for the second case :-

Where, 20th term is 64.

→ 64 = a + (20 - 1)d

→ 64 = a + 19d. . . . . (ii)

Subtracting eq.(i) by eq.(ii) as follows:-

a + 9d = 34

(-)

a + 19d = 64

→ -10d = -30

→ 10d = 30

→ d = 30/10

→ d = 3

∴ Common difference of the A. P. is 3

Now,

Dividing the terms by its common difference.

For 10th term :-

3)34(11

3

4

3

1

∴ Remainder is 1

And also for 20th term :-

3)64(21

6

4

3

1

∴ Remainder is 1

Hence, the remainder after dividing the terms by its common difference is 1