Determine k so that k+2, 4k-6 and 3k-2 are three consecutive terms of an AP | Class 10 | Arithmetic Progression

 

If an AP consist of n terms with first term a and nth term l. Show that of mth term from beginning and mth term from end is (a+l)

The sum of two numbers is 13/6. An even number of Airthmetic Means are being inserted between them and their sum exceeds their number by 1. Find the number of mean inserted.

✔️ Number of Arithmetic Means Inserted

12

Class 10 Airthmatic Pogression (AP) important Questions

📘 Q1 The sum of three numbers in Arithmetic Progression (A.P.) is 15 and the sum of the squares of the extreme terms is 58. Find the numbers.

✅ Answer: 3, 5, 7

📘 Q2 Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.

✅ Answer: 2, 4, 6, 8

If pth term of an A. P. s is q and it's qth term is p. Show that it's (p+q) th term is zero

Class 10 AP If sum of three number in AP is 9 and their product is 24, then number are

 

AP Math Class 12 question 101

 

The sum of four number IN an AP is 32 and the ratio of the product of the first and last term of the product of two middle term is 7 : 15, find the numbers

 

If the sum of the first n terms of an AP is 4n−n^2 , what is the first term (that is S1) ? What is the sum of first two terms ? What is the second term ? Similarly. find the 3rd and 10th and the nth terms.

 

Class 10 AP question | In an AP a=1, an=20, Sn= 399 then what is the value of n?

 

If θ1, θ2, θ3, ..., θn are in A.P., whose common difference is d, show that secθ1 secθ2 + secθ2 secθ3 + ... + secθn–1 secθn = (tanθn-tanθ1)/sin d

 

The sum of n natural number is 5n^2+4n, find its 8th term

ANSWER:  79

 

Class 10 Math AP MCQ Full Marks 30

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ANS Mathematics & Physics

Class 10 AP test full marks- 40

1. Can 2n^2 - 7 be the nth term of AP?  [2]
2. Show that the sum of (m+n)th and (m−n)th term of an A.P. is equal to twice the mth term. [4]
3. If the sum of first 7 terms of an AP is 49 and sum of 17 terms is 289, find the sum of first n terms. [3]
4. In an A.P. the first term is 25, n th term is −17 and the sum of n terms is 132. Find n and the common difference.  [3]
5. Divide 96 into four parts which are in A.P. and the ratio between the product of their means to the product of their extremes is 15:7. Find AP     [4]
6. If the sum of first m terms of an AP be n and the sum of its first n terms be m then show that the sum of its first (m+n) terms is −(m+n).   [extra]
7. How many three digit Numbers are divisible by 87?  [3]
8. In an AP ten times of its tenth term is equal to thirty times of 30th term. Find 40th term?  [3]
9. The first term of an A.P is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P. [3]
10. The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P and the sum of first 50 terms. [4]
11. In an A.P, if mth term is n and nth term is m, show that its rth term is (m + n - r). [3]
12. Given AP is 21,18,15....-81 Can any term of series be zero if yes find the no of terms. [2]
13. The sum of the 2nd term and the 7th term of an A.P is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P [3]
14. If 7 times the 7th term of an AP is equal to 11 times the 11th term, show that the 18th term of it is 0  [3]

Can 2n^2 - 7 be the nth term of AP

 

Show that the sum of (m+n)th and (m−n)th term of an A.P. is equal to twice the mth term.

 

In an A.P. the first term is 25, n th term is −17 and the sum of n terms is 132. Find n and the common difference.

 

If the sum of first 7 terms of an AP is 49 and sum of 17 terms is 289, find the sum of first n terms.

 

Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m−1)th numbers is 5:9. Find the value of m.

 

If the sum of first m terms of an AP be n and the sum of its first n terms be m then show that the sum of its first (m+n) terms is −(m+n).