Advertisements
Advertisements
प्रश्न
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
उत्तर
Let a and d be the first term and the common difference, respectively.
Now, a4 = 16 ......[Given]
⇒ a + 3d = 16 .....(i)
Also, a9 = 31 ......[Given]
⇒ a + 8d = 31 .....(ii)
Subtracting the equation (i) from equation (ii), we get
a + 8d = 31
a + 3d = 16
– – –
5d = 15
⇒ d = 3
Substituting the value of d in equation (i), w e get
a + 3 (3) = 16
⇒ a + 9 = 16
⇒ a = 16 – 9 = 7
Now, `"S"_n = n/2 [2a + (n - 1)d]`
∴ `"S"_35 = 35/2 [2(7) + (35 - 1)3]`
= `35/2 [14 + (34)3]`
= `35/2 (14 + 102)`
= `35/2 (116)`
= 35 × 58
= 2030
Hence, the sum of 35 terms of the A.P. is 2030.
APPEARS IN
संबंधित प्रश्न
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
In an AP given an = 4, d = 2, Sn = −14, find n and a.
The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
In a flower bed, there are 43 rose plants in the first row, 41 in second, 39 in the third, and so on. There are 11 rose plants in the last row. How many rows are there in the flower bed?
Find the three numbers in AP whose sum is 15 and product is 80.
Write the next term of the AP `sqrt(2) , sqrt(8) , sqrt(18),.........`
If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is ______.
The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.
Q.4
Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.
How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.
How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.
In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.)
If the nth term of an AP is (2n +1), then the sum of its first three terms is ______.
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?
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
