Question

Write the first three terms in each of the sequence defined by the fallowing (i) an = 3n+2 (ii) an = n2 +1 2. Write the first five terms of the sequence defined by an = (-1)n-1 . 2n 3. A sequence is defined by an = n3 -6n2 +11n-6 . show that the first three terms of the sequence are zero and all other terms are positive . 4. What is the 18th term of the sequence defined by an = . 5. Let a sequence be defined by a1=3 , an=3an-1 + 1 for all n > 1 . 6. Let a sequence be defined by a1 = 1 , a2 = 1 and , an = an-1 + an-2 for all n > 2 , find for n = 1 , 2 , 3 , 4 . 7. Write an A.P. whose first term is 10 and common difference is 3 . 8. Write an A.P. having 4 as the first term and -3 as the common difference . 9. Write an A.P. whose first term and common difference are -1.25 and -0.25 respectively . 10. For the fallowing arithmetic progressions write the first term and common difference (i) (ii) 0.6 , 1.7 , 2.8 , 3.9 , ........ 11. In which of the fallowing situations , the sequence formed will from an A.P. ? i) Number of students left in the school auditorium from the total strength of 1000 students when they leave the auditorium in batches of 25 . ii) The amount of the money in the account every year when Rs 100 are deposited annually to accumulate at compound interest at 4% per annum . 12. Find the common difference and write the next three terms of the A.P. 3,-2,-7,-12,..... 13. Find the 12th , 24th and the nth term of the A.P. given by 9 , 13 , 17 , 21 , 25 , ....... 14. Show that the sequence 9 , 12 , 15 , 18 , ...... is an A.P. find its 16th term and the general term. 15. The first term of an A.P. is -7 and the common difference 5 . Find its 18th term and the general term . 16. Determine the 10th term from the end of the A.P. 4 , 9 , 14 .... , 254 . 17. Which term of the sequence -1 , 3 , 7 , 11 ... is 95 ? 18. Which term of the sequence 4 , 9 , 14 , 19 ... , is 124 ? 19. How many terms are there in the sequence 3 , 6 , 9 , 12 , .... , 111 ? 20. For what value of n is the n th term of the fallowing two A.P’s the same ? i) 1, 7 , 13 , 19 , ... ii) 69 , 68 , 67 , .... 21. If the 8th term of an A.P. is 31 and the 15th term is 16 more than the 11th term , find the A.P. 22. Which term of the arithmetic progression 5 , 15 , 25 , ... will be 130 more than its 31st term ? 23. If the 10th term of the A.P. is 52 and 17th term is 20 more than the 13th term . find the A.P. 24. Is 184 a term of the sequence 3 , 7 , 11 , ... ? 25. Which term of the sequence 20 , 19 , 18 , 17 , ... is the first negative term ? 26. The 10th term of an A.P. is 52 and 16th term is 82 . Find the 32nd term and the general term . 27. The sum of 5th and 9th terms of an A.P. is 72 and the sum of 7th and 12th terms is 97 . Find A.P. 28. Determine the general term of an A.P. whose 7th term is -1 and 16th term 17 . 29. If five times the fifth term of an A.P. is equal to 8 times its eighth term , show that its 13th term is zero . 30. If the mth term of an A.P. be 1/n and nth term be 1/m , then show that its (mn)th term is 1 . 31. If the pth term of an A.P. is q and the qth term is P, prove that its nth term is (p+q-n) . 32. If m times the mth term of an A.P. is equal to n times its nth term , show that the (m+n)th term of the A.P. is zero . 33. If p th , qth , and rth terms of an A.P. are a , b , c respectively , then show that i) a (q-r) + b (r-p) + c (p-q) = 0 ii) (a-b) r + (b-c) p + ( c-a) q = 0 34. How many numbers of two digits are divisible by 7 ? 35. Find the number of integers between 50 and 500 which are divisible by 7 ? 36. Which term of the A.P. 3 , 15 , 27 , 39 , ... will be 132 more than its 54th term ? 37. Two A.P’s have the same common difference . The first term of one of these is 3 and that of the other is 8 . What is the difference between their ? i) 2nd terms ? ii) 4th terms ? iii) 10th terms ? iv) 30th terms ? 38. Two A.P’s have the same common difference . The difference between their 100th terms is 111 222 333 . What is the difference between their millionth terms ? 39. A sum of Rs 1000 is invested at 8% simple interest per annum . Calculate the interest at the end of 1 , 2 , 3 , ... years . Is the sequence of interest an A.P. ? Find the interest at the end of 30 years ?

Answer 1

Answer:

Step-by-step explanation:

3 , 15 , 27, 39.....

First we need to calculate 54th term

We know that

aₙ = a + (n -1 )d

Here, a =3

d = 15 -3 =12

n = 54

Putting values in formula

a₅₄ = a + (n-1)d

= 3 + (54-1) ₓ12

=3 + 53 ₓ 12

= 3 + 636

= 639

So 54th term a₅₄

132 + 639

= 771

Therefore aₙ = 771

Putting value in formula

aₙ = a + (n-1)d

771 = 3 +(n-1) ₓ 12

771 -3 = (n-1) ₓ 12

768 /12 = n-1

64 = n-1

n = 65

65th term is 132 more than 54th term