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Find t5 if a = 3 and d = –3.
Concept: General Term of an Arithmetic Progression
If a = 6 and d = 10, then find S10.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
How many two-digit numbers are divisible by 5?
Activity :- Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.
Here, d = 5, therefore this sequence is an A.P.
Here, a = 10, d = 5, tn = 95, n = ?
tn = a + (n – 1) `square`
`square` = 10 + (n – 1) × 5
`square` = (n – 1) × 5
`square` = (n – 1)
Therefore n = `square`
There are `square` two-digit numbers divisible by 5.
Concept: General Term of an Arithmetic Progression
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Complete the following activity to find the 19th term of an A.P. 7, 13, 19, 25, ........ :
Activity:
Given A.P. : 7, 13, 19, 25, ..........
Here first term a = 7; t19 = ?
tn + a + `(square)`d .........(formula)
∴ t19 = 7 + (19 – 1) `square`
∴ t19 = 7 + `square`
∴ t19 = `square`
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the sum of first 'n' even natural numbers.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the sum of all odd numbers between 351 and 373.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the middle term of the AP. 95, 86, 77, ........, – 247.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the sum of all even numbers from 1 to 250.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Sum of 1 to n natural number is 45, then find the value of n.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Complete the following table by writting suitable numbers and words.
| Sr.No | FV | Share is at | MV |
| (1) | Rs 100 | par | ... |
| (2) | ... | premium Rs 500 | Rs 575 |
| (3) | Rs 10 | ... | Rs 5 |
Concept: Shares
Mr.Amol purchased 50 shares of Face Value Rs100 when the Market value of the share was Rs 80. Company had given 20% dividend. Find the rate of return on investment.
Concept: Shares
Joseph purchased following shares, Find his total investment.
| Company A : 200 shares, | FV = Rs 2 | Premium = Rs 18 |
| Company B : 45 shares, | MV = Rs 500 | |
| Company C : 1 share, | MV = Rs 10,540. |
Concept: Shares
Fill in the blanks given in the contract note of sale-purchase of shares.
(B - buy S - sell)
|
No. of
shares
|
MV of
shares
|
Total
value
|
Brokerage
0.2%
|
9% CGST
on
brokerage
|
9% SGST
on
brokerage
|
Total
value of
shares
|
| 100 B | Rs 45 | |||||
| 75 S | Rs 200 |
Concept: Brokerage and Taxes on Share Trading
Smt. Mita Agrawal invested ₹ 10,200 when MV of the share is ₹ 100. She sold 60 shares when the MV was ₹ 125 and sold remaining shares when the MV was ₹ 90. She paid 0.1% brokerage for each trading. Find whether she made profit or loss? and how much?
Concept: Shares
Market value of shares and dividend declared by the two companies is given below. Face Value is same and it is Rs. 100 for both the shares. Investment in which company is more profitable ?
(1) Company A - Rs 132, 12%
(2) Company B - Rs 144, 16%
Concept: Shares
