Advertisements
Advertisements
प्रश्न
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
Advertisements
उत्तर
Given that,
a = 17
l = 350
d = 9
Let there be n terms in the A.P.
l = a + (n − 1) d
350 = 17 + (n − 1)9
9n = 350 + 9 - 17
9n = 359 - 17
9n = 342
⇒ n = `342/9`
⇒ n = 38
Sn = `n/2(a+l)`
Sn = `38/2(17+350)`
= 19 × 367
= 6973
Thus, this A.P. contains 38 terms and the sum of the terms of this A.P. is 6973.
APPEARS IN
संबंधित प्रश्न
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
Find the sum of first 40 positive integers divisible by 6.
Find the sum of first 15 multiples of 8.
Find the sum of the odd numbers between 0 and 50.
How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?
Find the sum of the first 40 positive integers divisible by 3
Find the sum 25 + 28 + 31 + ….. + 100
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
Find the middle term of the AP 10, 7, 4, ……., (-62).
If (2p +1), 13, (5p -3) are in AP, find the value of p.
Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and times the corresponding sides of ΔPQR?
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)
Write the sum of first n odd natural numbers.
The first term of an A.P. is p and its common difference is q. Find its 10th term.
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.
Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
If a = 6 and d = 10, then find S10
Find S10 if a = 6 and d = 3
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
If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are ______.
Find the sum:
1 + (–2) + (–5) + (–8) + ... + (–236)
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?
Hence find the sum of all the terms of the Arithmetic Progression (A.P.)
