Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 31

EASY

10th Tamil Nadu Board

IMPORTANT

Earn 100

If $6$ times of $6^{th}$ term of an A.P is equal to $7$ times the $7^{th}$ term, then the $13^{th}$ term of the A.P. is

12.5% studentsanswered this correctly

Important Questions on Numbers and Sequences

EASY

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 32

If the sequence

t_{1}, t_{2}, t_{3}, \dots \dots \dots . .

are in A.P. then the sequence

t_{6,} t_{12}, t_{18}, \dots \dots

is

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 33

If

(m + 1)^{t h}

term of an A.P. is twice the

(n + 1)^{t h}

term, then prove that

(3 m + 1)^{t h}

term is twice the

(m + n + 1)^{t h}

term.

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 34

Two A.P.'s have the same common difference. The first term of one A.P. is

2

and that of the other is

7

Show that the difference between their

10^{t h}

terms is the same as the difference between their

21^{s t}

terms, which is the same as the difference between any two corresponding terms.

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 35

Check whether the sequence $a - 3, a - 5, a - 7, . . \dots$ in $AP$ or not?.

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 36

Check whether the sequence $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{4}, \dots \dots \dots$ is in $AP$ or not?

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 37

The ratio of the sums of

m

and

n

terms of an A.P. is

m^{2} : n^{2}

. Show that the ratio of

m^{t h}

and

n^{t h}

term is

(2 m - 1) : (2 n - 1)

.

HARD

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 38

If the sum of

n

terms of an A.P. is

3 n^{2} + 5 n

and its

m^{t h}

term is

164,

find the value of

m .

MEDIUM

10th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Numbers and Sequences>Exercise>Q 39

A man starts repaying a loan as first installment of

₹ 100

. If he increases the installment by

₹ 5

every month, what amount he will pay in the

3 0^{t h}

installment?