Question
Write the arithmetic progression when first term a and common difference d are as following:
$\text{a}=-1,\text{d}=\frac{1}{2}$
$\text{a}=-1,\text{d}=\frac{1}{2}$
✓
Answer
$\text{a}=-1,\text{d}=\frac{1}{2}$
Now, as $a = -1$
A.P. would be represented by $a, a_1, a_2, a_3, a_4, .....$
So,
$a_1 = a + d$
$\text{a}_1=-1+\Big(\frac{1}{2}\Big)$
$\text{a}_1=\frac{-2+1}{2}$
$\text{a}_1=\frac{-1}{2}$
Similarly.
$a_2 = a_1 + d$
$\text{a}_2=\frac{-1}{2}+\Big(\frac{1}{2}\Big)$
$a_2 = 0$
Also,
$a_3 = a_2 + d$
$\text{a}_3=0+\Big(\frac{1}{2}\Big)$
$\text{a}_3=\frac{1}{2}$
Further,
$a_4 = a_3 + d$
$\text{a}_4=\Big(\frac{1}{2}\Big)+\Big(\frac{1}{2}\Big)$
$\text{a}_4=\frac{2}{2}$
$\text{a}_4=1$
Therefore, A.P. with $a = -1$ and $\text{d}=\frac{1}{2}$ is $-1,\frac{-1}{2},0,\frac{1}{2},1\ .....$
Now, as $a = -1$
A.P. would be represented by $a, a_1, a_2, a_3, a_4, .....$
So,
$a_1 = a + d$
$\text{a}_1=-1+\Big(\frac{1}{2}\Big)$
$\text{a}_1=\frac{-2+1}{2}$
$\text{a}_1=\frac{-1}{2}$
Similarly.
$a_2 = a_1 + d$
$\text{a}_2=\frac{-1}{2}+\Big(\frac{1}{2}\Big)$
$a_2 = 0$
Also,
$a_3 = a_2 + d$
$\text{a}_3=0+\Big(\frac{1}{2}\Big)$
$\text{a}_3=\frac{1}{2}$
Further,
$a_4 = a_3 + d$
$\text{a}_4=\Big(\frac{1}{2}\Big)+\Big(\frac{1}{2}\Big)$
$\text{a}_4=\frac{2}{2}$
$\text{a}_4=1$
Therefore, A.P. with $a = -1$ and $\text{d}=\frac{1}{2}$ is $-1,\frac{-1}{2},0,\frac{1}{2},1\ .....$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The total value (with GST) of a remote-controlled toy car is Rs. 1770. Rate of GST is 18% on toys. Find the taxable value, CGST and SGST for this toy-car.
Is 5, 8, 11, 14, …. an A.P.? If so then what will be the 100th term? Check whether 92 is in this A.P.? Is number 61 in this A.P.?
Height of a solid cylinder is 10cm and diameter 8cm. Two equal conical hole have been made from its both ends. If the diameter oaf the holes is 6cm and height 4cm, find
- volume of the cylinder
- volume of one conical hole,
- volume of the remaining solid.
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = x^2+ px + q$, find a quadratic polynomial whose zeroes are:
→→- $\alpha+2 ,\beta+2$
- $\frac{\alpha-1}{\alpha+1},\frac{\beta-1}{\beta+1}.$
In an A.P., if the $5^{\text {th }}$ and 12 th terms are 30 and 65 respectively, what is the sum of the first 20 terms.
→The graph of the equations 2 ? − ? − 4 = 0 and ? + ? + 1 = 0 intersect each other in point P (a, b) then find the coordinates of P?
Solve the following quadratic equations by factorization:
$\frac{\text{x}-1}{\text{x}-2}+\frac{\text{x}-3}{\text{x}-4}=3\frac{1}{3},$ $\text{x}\neq2, 4$
→$\frac{\text{x}-1}{\text{x}-2}+\frac{\text{x}-3}{\text{x}-4}=3\frac{1}{3},$ $\text{x}\neq2, 4$
A horse is placed for grazing inside a reangular field 70m by 2m. It is tethered to one comer by a rope 21m long. On how much area an it graze? How much area is left ungrazed? $\Big[\text{Use }\pi=\frac{22}{7}\Big]$
→In a $\triangle\text{ABC},$ right angled at A, if $\tan\text{C}=\sqrt{3},$ find the value of sin B cos C + cos B sin C.
→