Advertisements
Advertisements
प्रश्न
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
Advertisements
उत्तर
Let a and d be the first term and common difference, respectively of an AP.
∵ Sum of n terms of an AP,
Sn = `n/2 [2a + (n - 1)d]` ...(i)
Now, S6 = 36 ...[Given]
⇒ `6/2[2a + (6 - 1)d]` = 36
⇒ 2a + 5d = 12 ...(ii)
And S16 = 256
⇒ `16/2[2a + (16 - 1)d]` = 256
⇒ 2a + 15d = 32 ...(iii)
On subtracting equation (ii) from equation (iii), we get
10d = 20
⇒ d = 2
From equation (ii),
2a + 5(2) = 12
⇒ 2a = 12 − 10 = 2
⇒ a = 1
∴ S10 = `10/2 [2a + (10 - 1)d]`
= 5[2(1) + 9(2)]
= 5(2 + 18)
= 5 × 20
= 100
Hence, the required sum of first 10 terms is 100.
APPEARS IN
संबंधित प्रश्न
How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?
Divide 32 into four parts which are in A.P. such that the product of extremes is to the product of means is 7 : 15.
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
In an AP given d = 5, S9 = 75, find a and a9.
A small terrace at a football field comprises 15 steps, each of which is 50 m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (See figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = `1/4 xx 1/2 xx 50 m^3`]
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
Find the sum 3 + 11 + 19 + ... + 803
What is the sum of first n terms of the AP a, 3a, 5a, ....
Find the sum of the following APs:
9, 7, 5, 3, ... to 14 terms.
The nth term of an A.P. is given by (–4n + 15). Find the sum of first 20 terms of this A.P.
Choose the correct alternative answer for the following question .
First four terms of an A.P. are ....., whose first term is –2 and common difference is –2.
If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + ....\]
The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹ 50 in the first month of this year and increased her monthly saving by ₹ 20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
Write the sum of first n odd natural numbers.
Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is
How many terms of the A.P. 27, 24, 21, ..., should be taken so that their sum is zero?
Find the sum of three-digit natural numbers, which are divisible by 4.
What is the sum of an odd numbers between 1 to 50?
First four terms of the sequence an = 2n + 3 are ______.
Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.
Find the sum of the integers between 100 and 200 that are not divisible by 9.
Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30th installment? What amount of loan has he paid after 30th installment?
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
When the first term a, the number of terms n and the common difference d are known, which formula gives the sum of the first n terms of an Arithmetic Progression?
