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ARITHMETIC PROGRESSIONS - Truw/False

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Q 01 / 25

In an arithmetic progression (AP), the difference between consecutive terms is constant.

✔ True ✘ False

Q 02 / 25

The first term of an AP is always denoted byaaa.

✔ True ✘ False

Q 03 / 25

If the common differencedddis negative, the AP is always decreasing.

✔ True ✘ False

Q 04 / 25

The nth term of an AP is given by \(a_n=a+(n-1)d\).

✔ True ✘ False

Q 05 / 25

The sum of the first n terms of an AP can be \(S_n = \frac{n}{2} [2a + (n-1)d]\).

✔ True ✘ False

Q 06 / 25

Every sequence of numbers is an arithmetic progression.

✔ True ✘ False

Q 07 / 25

In an AP with 5 terms, the middle term is the arithmetic mean of all terms.

✔ True ✘ False

Q 08 / 25

If three numbers in AP have sum 24 and middle term 8, they are 4, 8, 12.

✔ True ✘ False

Q 09 / 25

The common difference can be zero in an AP.

✔ True ✘ False

Q 10 / 25

The 10th term from the end of an AP with 20 terms equals the 11th term from the start.

✔ True ✘ False

Q 11 / 25

\(S_n = \frac{n}{2} (first\ term + last\ term)\) applies only to increasing APs.

✔ True ✘ False

Q 12 / 25

If the sum of first 10 terms is 100 and first term is 5, thendddmust be positive.

✔ True ✘ False

Q 13 / 25

In AP 3, 6, 9, ..., the 100th term exceeds 300.

✔ True ✘ False

Q 14 / 25

The number of terms in AP 2, 5, 8, ..., 26 is 10.

✔ True ✘ False

Q 15 / 25

If a, b, c are in AP, then 2b = a + c.

✔ True ✘ False

Q 16 / 25

The sum \(S_{2n} = 2 S_n\) for any AP.

✔ True ✘ False

Q 17 / 25

In AP with \(a=1,\ d=2,\ S_5 = 35\).

✔ True ✘ False

Q 18 / 25

An AP can have fractional common difference.

✔ True ✘ False

Q 19 / 25

The last term l of AP is \(a + n d\).

✔ True ✘ False

Q 20 / 25

If 5 terms in AP sum to 25, average term is 5.

✔ True ✘ False

Q 21 / 25

Sequence 1, 1, 1, 2, 2, 3, 3 is an AP.

✔ True ✘ False

Q 22 / 25

For AP 10, 7, 4,..., sum of first 10 terms is negative.

✔ True ✘ False

Q 23 / 25

\(n\)th term from end is \(l - (n-1)d\).

✔ True ✘ False

Q 24 / 25

\(S_n\) formula assumes positive terms only.

✔ True ✘ False

Q 25 / 25

If \(d=0,\ S_n = n a\).

✔ True ✘ False

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