Arithmetic Progressions Practice 2: Sum of Terms

Section A: Sum Formula Concepts

Question 1mcq

Why can the sum of an AP be found by pairing terms from the beginning and the end?

A.Each pair has the same sum.

B.Each pair has the same product.

C.The common difference becomes zero.

D.The first term must equal the last term.

Question 2mcq

For

2+5+8+11+14

, which pairing best explains the AP sum idea?

A.

2+5

,

8+11

B.

2+14

,

5+11

, and middle term

8

C.

2\times14

,

5\times11

D.

14-2

,

11-5

Question 3mcq

Find the sum of the first

10

terms of the AP

3, 7, 11, \ldots

.

A.

180

B.

190

C.

200

D.

210

Question 4mcq

Find

S_{20}

for the AP with

a=5

and

d=3

.

A.

620

B.

640

C.

670

D.

700

Question 5mcq

A student calculates

S_{12}

for

4,10,16,\ldots

as

\frac{12}{2}[2(4)+12(6)]

. What is the error?

A.They used

n

instead of

n-1

.

B.They used the wrong first term.

C.They should divide by

12

.

D.They changed the common difference sign.

Section B: Calculate and Check Sums

Question 6mcq

Find the sum of

15

terms of an AP whose first term is

6

and last term is

48

.

A.

405

B.

410

C.

420

D.

430

Question 7mcq

An AP has

20

terms. The first term is

3

and the last term is

79

. What is the sum?

A.

780

B.

800

C.

820

D.

840

Question 8mcq

The first

n

natural numbers form the AP

1,2,3,\ldots,n

. What is the sum of the first

50

natural numbers?

A.

1225

B.

1250

C.

1275

D.

2500

Question 9mcq

The sum of

n

terms is found using

S_n=\frac{n}{2}(a+l)

. Which information is enough to use this directly?

A.

a,d,n

only

B.

a,l,n

C.

d,l

only

D.

a,d

only

Question 10mcq

Assertion: In an AP, the average of the first and last terms equals the average of all terms. Reason: Opposite terms pair to the same sum. Which is correct?

A.Both are true and the reason explains the assertion.

B.Both are true but the reason does not explain it.

C.Assertion is true but reason is false.

D.Assertion is false but reason is true.