Find the sum of first $25$ multiples of $6$.

Important Questions on Arithmetic Progression (AP)

MEDIUM

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 6 - Arithmetic Progression (AP)>EXERCISE 6.2>Q 8

Find the sum of all the multiples of $7$ between $100$ and $300$.

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 6 - Arithmetic Progression (AP)>EXERCISE 6.2>Q 9

If the ${12}^{th}$ term of an AP is $-13$ and the sum of the first four terms is $24$, find the sum of the first $15$ terms.

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 6 - Arithmetic Progression (AP)>EXERCISE 6.2>Q 10

Find the sum of the first $22$ terms of an AP whose $8^{th}$ and ${16}^{th}$ terms are respectively $37$ and $85$.

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 6 - Arithmetic Progression (AP)>EXERCISE 6.2>Q 11

The sum of the first 7 terms of an AP is 10 and that of the next 7 terms is 17. Find the first term and the common difference of the AP.

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 6 - Arithmetic Progression (AP)>EXERCISE 6.2>Q 12

Find the sum of the first $50$ terms of an AP whose ${\mathrm{n}}^{\mathrm{th}}$ term is $3-2\mathrm{n}$.

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 6 - Arithmetic Progression (AP)>EXERCISE 6.2>Q 13

Find the first term and the common difference of an AP if the sum of the first $\mathrm{n}$ term is $\frac{\mathrm{n}\left(5\mathrm{n}+7\right)}{12}$.

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 6 - Arithmetic Progression (AP)>EXERCISE 6.2>Q 14

In an AP, if the sum of the first $\mathrm{m}$ terms is equal to $\mathrm{n}$ and that of the first $\mathrm{n}$ terms is equal to $\mathrm{m}$, then prove that the sum of the first $\left(\mathrm{m}+\mathrm{n}\right)$ terms is $-(\mathrm{m}+\mathrm{n})$.

HARD

10th Manipur Board

IMPORTANT

Mathematics for Class 10>Chapter 6 - Arithmetic Progression (AP)>EXERCISE 6.2>Q 15

The sum of the first $\mathrm{n}, 2\mathrm{n}, 3\mathrm{n}$ terms of an AP are ${\mathrm{S}}_1, {\mathrm{S}}_2, {\mathrm{S}}_3$ respectively. Show that ${\mathrm{S}}_3=3({\mathrm{S}}_2-{\mathrm{S}}_1)$.