Class 10 (All in one) – Arithmetic ProgressionContact Number: 9667591930 / 8527521718

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Find the next term of the AP : 3, 1, –1, –3, …

Find the common difference of the AP : $\frac{1}{p}$, $\frac{1-p}{p},\text{\hspace{0.17em}}\frac{1-2p}{p},\text{\hspace{0.17em}}$ …

For what value of *k* will *k* + 9, 2*k* – 1 and 2*k* + 7 are the consecutive terms of an AP.

Find the 19th term of the following sequence.

${t}_{n}=\{\begin{array}{l}{n}^{2},\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}where}n\text{ineven}\\ {\text{n}}^{2}-1,\text{\hspace{0.17em}\hspace{0.17em}where}n\text{isodd}\end{array}$

For an AP, if *a*_{18} – *a*_{14} = 32, then find the common difference *d*.

What is the sum of all natural numbers from 1 to 100?

Find the 15th term of the AP: y – 7, y – 2, y + 3, …

Find the 7th term of the sequence whose *n*th term is given by *a _{n}* = (–1)

Find the 25th term of the AP : $-5,\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}-\frac{5}{2},\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}0,\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\frac{5}{2},\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{...}$

If the *n*th term of an AP is(2*n* + 1), then find the sum of its first three terms.

If the common difference of an AP is 3, then find *a*_{20} – *a*_{15}.

If $\frac{1+3+5+\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{...}\text{\hspace{0.17em}upto\hspace{0.17em}}n\text{\hspace{0.17em}terms}}{2+5+8+\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{...}\text{\hspace{0.17em}upto\hspace{0.17em}\hspace{0.17em}}n\text{\hspace{0.17em}terms}}$= 9. then find the value of *n*.

If 21, *a*, *b* and – 3 are in AP, then find the value of (*a* + *b*).

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

The 4th term of an AP is zero. Prove that the 25th term of the AP is three times its 11th term.

The fourth term of an AP is 11. The sum of the fifth and seventh terms of the AP is 24. Find its common difference.

Find the sum of all three-digit natural numbers, which are multiples of 11.

The nth term of an AP is *a _{n}* =2

The 16th term of an AP is 1 more than twice its 8th term. If the 12th term of an AP is 47, then find its *n*th term.

Find the sum of first 24 terms of the AP *a*_{1}, *a*_{2}, *a*_{3} ..., if it is known that *a*_{1} + *a*_{5} + *a*_{10} + *a*_{15} + *a*_{20} + *a*_{24} = 225

Find the sum of all multiple of 7 lying between 500 and 900.

Find the sum of all two-digit numbers greater than 50 which when divided by 7 leaves remainder 4.

Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.

The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, then find the AP.

If 12th term of an AP is 213 and the sum of its four terms is 24, then what is the sum of its first 10 terms?

Sum of the first n terms of an AP is 5*n*^{2} – 3*n*. Find the AP and also find its 16th term.

The sum of first, third and seventeenth terms of an AP is 216. Find the sum of the first 13 terms of the AP.

If four numbers are in AP such that their sum is 50 and the greatest number is 4 times the least, then find the numbers.

If there are (2*n* + 1) terms in an AP, then prove that the ratio of the sum of odd terms and the sum of even terms is (*n* + 1) : *n*.

Find the number of terms in the sequence 20, $19\frac{1}{3},\text{\hspace{0.17em}\hspace{0.17em}}18\frac{2}{3},$ …, of which the sum is 300.

Explain the double answer.

The sum of the first term and the fifth term of an ascending AP is 26 and the product of the second term by the fourth term is 160. Find the sum of the first seven terms of this AP.

Find the common difference

Find the common difference of an AP whose first term is 5 and the sum of its first 4 terms is half the sum of the next 4 terms.

The sum of first *n*, 2*n* and 3*n* terms of an AP are *S*_{1}, *S*_{2} and *S*_{3}, respectively. Prove that *S*_{3} = (*S*_{2} – *S*_{1}).

The sum of first *n* terms of three APs are *S*_{1} *S*_{2}, and *S*_{3}. The first term of each AP is unity and their common differences ate 1, 2 and 3, respectively.

Prove that *S*_{1} + *S*_{3} = 2*S*_{2}.

Each year, a tree grows 5 cm less than it did the preceding year. If it grew by 1m in the first year, then in how many years will it have ceased growing?

Jaspal Singh repays his total loan of ₹118000 by paying every month starting with the first instalment of ₹1000. If he increases the instalment by ₹100 every month, then what amount will be paid by him in the 30th instalment? What amount of loan does he still have to pay after 30th instalment?

Solve the equation –4 + (–1) + 2 + ... + *x* = 437.

If the *m*th term of an AP is $\frac{1}{n}$ and *n*th term is $\frac{1}{m}$, then show that the sum of *mn* terms is $\frac{1}{2}$(*mn* + 1).

The sum of the first *p*, *q*, *r* terms of an AP are *a*, *b* and *c*, respectively. Show that $\frac{a}{p}(p-r)+\frac{b}{q}(r-p)+\frac{c}{r}(p-q)=0.$

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7 : 15. Find the numbers.

If *a*_{1} *a*_{2}, …, *a _{n}*

The ratio of the sums of first *m* and *n* terms of an AP is *m*^{2} : *n*^{2}. Show that the ratio of the *m*th and *n*th terms is (2*m* – 1) : (2*n* – 1).

Ram asks the labour to dig a well upto a depth of 10 m. Labour charges ₹ 150 for first metre and ₹ 50 for each subsequent metres. As labour was uneducated, he claims ₹ 550 for the whole work.

(i) What should be the actual amount to be paid to the labour?

(ii) What value of Ram is depicted in the question, if he pays ₹ 600 to the labour?

Nidhi saves ₹ 2 on first day of the month, ₹ 4 on second day, ₹ 6 on third day, and so on.

(i) What will be her savings in the month of February 2012?

(ii) What value is depicted by Nidhi?

Mamta has two options to buy a house

(i) She can pay a lumpsum amount of ₹ 2200000.

(ii) She can pay ₹ 400000 cash and balance in 18 annual instalments of ₹ 100000 plus 10% interest on the unpaid amount.

She prefers the option (i) and donates 50% of the difference of the costs in the above two options to National Relief Fund.

(a) What amount was donated to National Relief Fund?

(b) By choosing to pay a lumpsum amount and donating 50% of the difference to National Relief Fund, which value is depicted by Mamta?

If the sum of first p terms of an AP is *q* and the sum of first *q* terms is *p*, then find the sum of first (*p* + *q*) terms.

The sum of first six terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1: 3. Calculate the first and the 13th term of the AP.

A man arranges to pay off a debt of ₹3600 by 40 annual instalments which are in AP. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid. Find the value of the 8th instalment.

The sum of the first five terms and the sum of the first seven terms of an AP is 167. If the sum of the first ten terms of this AP is 235, then find the sum of its first twenty terms.

In the given figure, AB || PQ || CD, AB = x units, CD = y . units and PQ = z units. Prove that *. **CBSE 2015**

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