Arithmetic sequence examples with answer Grade 10

Grade 10 Math Module 1 searching for patterns, sequence and series from Jocel Sagario

The arithmetic sequence is a series of numbers which increases or decreases. The sequence increases or decreases by a fixed amount. This fixed amount is known as common difference. To look for any term in the arithmetic sequence, use the arithmetic sequence formula.

(1)  Check whether the following sequences are in A.P.

(i) a - 3, a - 5, a -7,...         Solution

(ii)  1/2, 1/3, 1/4, 1/5........      Solution

(iii) 9, 13, 17, 21, 25,...      Solution

(iv) -1/3, 0, 1/3, 2/3.........      Solution

(v) 1, -1, 1, -1, 1, -1,............      Solution

(2)  First term a and common difference d are given below. Find the corresponding A.P.

(i) a = 5 , d = 6          Solution

(ii) a = 7 , d =−5          Solution

(iii) a = 3/4, d = 1/2         Solution

(3)  Find the first term and common difference of the Arithmetic Progressions whose nth terms are given below

(i) tn = −3 +2n       Solution

(ii) tn = 4 - 7n     Solution

(4)  Find the 19th term of an A.P. -11,-15,-19,...     Solution

(5)  Which term of an A.P. 16, 11, 6, 1,... is -54 ? 

Solution

(6)  Find the middle term(s) of an A.P. 9, 15, 21, 27,…,183.

Solution

(7)  If nine times ninth term is equal to the fifteen times fifteenth term, show that six times twenty fourth term is zero.           Solution

(8)  If 3 + k, 18 - k, 5k + 1 are in A.P. then find k.  Solution

(9)  Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P.    Solution

(10)  In a theatre, there are 20 seats in the front row and 30 rows were allotted. Each successive row contains two additional seats than its front row. How many seats are there in the last row?      Solution

(11)  The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms. 

 Solution

(13)  The ratio of 6th and 8th term of an A.P. is 7:9. Find the ratio of 9th term to 13th term.         Solution

(14)  In a winter season let us take the temperature of Ooty from Monday to Friday to be in A.P. The sum of temperatures from Monday to Wednesday is 0° C and the sum of the temperatures from Wednesday to Friday is 18° C. Find the temperature on each of the five days.

Solution

(15)  Priya earned ₹15,000 in the first month. Thereafter her salary increased by ₹1500 per year. Her expenses are ₹13,000 during the first year and the expenses increases by ₹900 per year. How long will it take for her to save ₹20,000 per month.                    Solution 

Step 2. To draw the front face, join 8 dots to form the length of the cuboid and 3 adjacent dots to form its breadth as shown:

Step 3. From the corners of the rectangle drawn above, draw 4 parallel line segments as shown below:

Step 4. Join the corners of the image together as shown below:

5. According to the convention redraw the hidden edges as dotted lines as shown:

This isometric sketch representing a cuboid of dimension 8 × 3 ×3. Thus, using an isometric dot sheet, we can draw three-dimensional shapes of exact measurements or dimensions without any ambiguity.

Thus, isometric sketches of different shapes can be drawn easily.

Related Articles

• Cuboid and Cube
• Square
• Rectangle
• Difference Between Cube and Cuboid
• Difference Between Square and Rectangle

Learn more about the isometric sketch and other solid shapes download BYJU’S- The Learning App from Google Play Store. Join us and fall in love with learning.

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