Class 11

Math

Algebra

Sequences and series

Let $a_{1},a_{2},a_{3},...$ be in an $A.P.$ with common difference not a multiple of $3$, Then maximum number of consecutive terms so that all are primes is

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Sides of a triangle ABC are in A.P if a < minimum {b,c}, then cos A is equal to:

The interior angles of a polygon are in A.P if the smallest angle be $120_{∘}$ and the common difference be 5, then the number of sides is

If the $8_{th}$ term of an A.P. is $31$ and the $15_{th}$ term is $16$ more than the $11_{th}$ term, find the A.P.

Find out the arithmetic progression formed when $4$ is multiplied to each term of the arithmetic progression $8,6,4,2,...$ Also find out the arithmetic progression when each term of the above A.P. is divided by $4$. Comment on the common difference of the new A.P.

The number of divisors of $1549,122$ and $1029$ are in

If $x$ is the $n_{th}$ term of the $AP:521 ,11,1621 ,22......$ with $x=550,$ find $_{′}n_{′}$.

The sum of $4_{th}$ and $8_{th}$ term of an A.P. is 24 and the sum of $6_{th}$ and $10_{th}$ term is 34. Find the first term and the common difference of A.P.

All the term of an A. P. are natural numbers and the sum of the first $20$ terms is greater than $1072$ and less than $1162$. If the sixth term is $32$ then-