# Recent questions tagged arithmetic-progression

1
Three positive integers $x,y$ and $z$ are in arithmetic progression. If $y – x 2$ and $xyz = 5(x+y+z),$ then $z-x$ equals$12$$8$$14$$10 1 answer 2 If (2n+1)+(2n+3)+(2n+5)+\dots+(2n+47)=5280, then what is the value of 1+2+3+\dots+n _______ 1 answer 3 The number of common terms in the two sequences: 15, 19, 23, 27,\dots,415 and 14, 19, 24, 29,\dots,464 is18$$19$$21$$20$
The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots$ + $95 \times 99$ is$80707$$80773$$80730$$80751 1 answer 5 Let a_{1},a_{2},\dots , a_{52} be a positive integers such that a_{1}<a_{2}<\dots < a_{52}. Suppose, their arithmetic mean is one less than the arithmetic mean of a... 1 answer 6 Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ... 1 answer 7 If \log\left ( 2^{a} \times 3^{b}\times 5^{c}\right ) is the arithmetic mean of \log\left ( 2^{2} \times 3^{3}\times 5 \right ), \log\left ( 2^{6} \times3\times 5^{7... 1 answer 8 If the square of the 7^{\text{th}} term of an arithmetic progression with positive common difference equals the products of the 3^{\text{rd}} and 17^{\text{th}} ter... 1 answer 9 Let a_{1}, a_{2},\ldots, a_{3n} be an arithmetic progression with a_{1} = 3 and a_{2}=7. If a_{1}+ a_{2}+\ldots +a_{3n}=1830, then what is the smallest positive... 0 answers 10 A series \text{S1} of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series \text{S2... 0 answers 11 A series \text{S1} of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series \text{S2... 2 answers 12 Fourth term of an arithmetic progression is 8. What is the sum of the first 7 terms of the arithmetic progression?7$$64$$56Cannot be determined 1 answer 13 Consider the set \text{S} = \left \{ 1, 2, 3, \dots,1000 \right \}. How many arithmetic progressions can be formed from the elements of \text{S} that start with 1 a... 1 answer 14 If a_{1},a_{2}\dots are in A.P., then, \frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\dots+\frac{1}{\sqrt{a_{n}}+\sqrt{a_{n+1}}} is equal to... 0 answers 15 if \log_3\left(2^x - 5\right), \: \log_3\left(2^x - \frac{7}{2}\right) are in arithmetic progression, then the value of x is equal to5$$4$$2$$3$
The sum of $3$-rd and $15$-th elements of an arithmetic progression is equal to the sum of $6$-th, $11$-th and $13$-th elements of the same progression. Then which elemen...
If the sum of first $11$ terms of an arithmetic progression equals that of a first $19$ terms, then what is the sum of the first $30$ terms?$0$$-1$$1$Not unique
Consider the set $\text{S} = \{1, 2, 3, \dots, 1000\}.$ How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ and with $1000$...