Advertisements
Advertisements
प्रश्न
Mark the correct alternative in each of the following:
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
पर्याय
87
88
89
90
Advertisements
उत्तर
In the given problem, we are given 7th and 13th term of an A.P.
We need to find the 26th term
Here,
a7 = 34
a13 = 64
Now, we will find a7 and a13 using the formula
an = a + (n-1) d
So,
a7 = a + (7 - 1 ) d
34 = a + 6d .............(1)
Also,
`a_13 = a + (13 - 1 ) d`
64 = a + 12 d ........(2)
Further, to solve for a and d
On subtracting (1) from (2), we get
64 - 34 = (a + 12d) - (a + 6d)
30 = a + 12d - a -6d
30 = 6d
`d = 30/6`
d = 5 ................(3)
Substituting (3) in (1), we get
34 = a + 6(5)
34 = a + 30
a = 34 - 30
a = 4
Thus,
a = 4
d = 5
So, for 18th term (n = 18),
Substituting the above values in the formula, an = a + (n-1) d
a18 = 4 + (18 - 1) 5
= 4 + 17 (5)
= 4 + 85
= 89
Therefore, a18 = 89
APPEARS IN
संबंधित प्रश्न
Find the sum of the following arithmetic progressions:
1, 3, 5, 7, ... to 12 terms
Find the sum of the following arithmetic progressions:
a + b, a − b, a − 3b, ... to 22 terms
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.
The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference.
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.
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
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.
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
Write the common difference of an A.P. whose nth term is an = 3n + 7.
Write the nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
The common difference of the A.P.
Mrs. Gupta repays her total loan of Rs. 1,18,000 by paying installments every month. If the installments for the first month is Rs. 1,000 and it increases by Rs. 100 every month, What amount will she pays as the 30th installments of loan? What amount of loan she still has to pay after the 30th installment?
How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?
In a ‘Mahila Bachat Gat’, Sharvari invested ₹ 2 on first day, ₹ 4 on second day and ₹ 6 on third day. If she saves like this, then what would be her total savings in the month of February 2010?
The sum of all two digit odd numbers is ______.
Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
