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GUIDANCE TUITION CENTRE


ALAKODE

MONTHLY EXAM-1

MATHEMATICS



TIME:2HRS

MARK:100



1. 5x-6. 3x and 7x-18 are three consecutive terms of an AP.Find middle term by finding the value of x



2. nth term of an AP is 12-2n

a. what is the common difference?

b. What is the first term

c. Write AP?

d. Find its 20 th term

e. Is -188 a term of this AP? Why?

f. Find the sum of first 50 terms of this AP?

3. The sum of the first and 50th t terms of an AP is x.Find the sum of the 25th and 26th terms of the progression?



4. sum of n terms of an AP is n²+2n.

g. Find AP?

h. What is the common difference?

i. Find the sum of the first 15 terms of it?



5. Three numbers are in the ratio 3:4:6. If 9 is subtracted from the third number, they are in AP.Find the numbers?



6. Calculate the sum of all integers between 150 and 450 which are exactly divisible by 11?



7. The sum of first 19 terms of an AP is 339.find its 10th term?



8. If the sum of three consecutive terms of an AP is 33 and product is 935, then find AP?



9. From a progression of the numbers between 300 and 700 which leaves a remainder 2on dividing by 6.form another progression with numbers between 300 and 700 which leaves a remainder 5 on dividing by 6. what is the difference between the sum of terms of these two progressions



10. The mth term of AP is n . nth term is m . what is the common difference?



11. A tomb is being constructed using bricks. 5000 bricks were required for the foundation step. 4875 bricks were required in the second steps. 4750 bricks in the third step and so on .find the total number of bricks used to construct the tomb? It was decided to increase the height of the tomb by 6 more steps. How many more bricks are required to complete the tomb? What is the number of bricks in the top most of the on tended tomb?



12. What is the difference between 20th terms of two arithmetic progressions with same common difference and first terms 3 and 8 ?Justify your answer.



13. In a shop soaps are arranged in rows one above the other there are 31 soaps at the bottom row ,29 above it and 27 above it and so on .if the top most row contains only one soap,find total number of soaps?



14. . Find the sum of first 30 terms of an A. P. whose nth term is 2 + 1/2n



15. Which term of the sequence 114, 109, 104 .... is the first negative term ?



16 what is the midterm of the AP with first term 4 and common difference 7?.find the sum of first term and last term of this AP?



17. 1 ,4 ,7 ,10 ,13 ,16 ,19…………………

4 ,8 12 ,16 ,20 ,28………………………

7 ,12 ,17 ,22 ,27……………………..

10 ,16 ,22 ,28 ,34…………….

…………………………

……………………………………

There are 21 rows in this method

What is the first term of 21st row ?

What is the common difference of 21st row?

Find the sum of first 41 terms of 21st row?



18. 15th term is 65 more than 10th term of an AP with first term 21,

a. what is common difference?

b. what is the nth term?

c. is 398 a term of this AP? Why?



19. Write an AP with first term ‘x’ and common difference ‘x’. Find the sum of the first 40 terms of this AP?



20. In an AP the 10th term is same as 40 added to its 5th term The 15th term of this progression is 127.Find common difference and first term ?



21. Write down the AP with common difference 6 .State whether 75 can be the difference between any two terms of this progression .Why?