Advertisements
Advertisements
Question
For arithmetic progression, first term is – 8 and last term is 55. If sum of all these terms is 235, find the number of terms and common difference.
Solution
Let a and d represent the first term and common difference, respectively.
So, a = – 8, an = 55 , and Sn = 235
We know, `S_n = n/2 (a + a_n)`
⇒ 235 = `n/2(-8 + 55)`
⇒ 470 = n(47)
⇒ n = 10
Now, an = a + (n – 1)d
⇒ 55 = – 8 + (10 – 1)d
⇒ 55 + 8 = 9d
⇒ 63 = 9d
⇒ d = 7
Hence, the number of terms is 10 and common difference is 7.
APPEARS IN
RELATED QUESTIONS
If m times mth term of an A.P. is equal to n times its nth term, then show that (m + n)th term of the A.P. is zero.
The 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term and the general term
If pth , qth and rth terms of an A.P. are a, b, c respectively, then show that
(i) a (q – r) + b(r – p) + c(p – q) = 0
(ii) (a – b) r + (b –¬ c) p + (c – a) q = 0
In the following situation, involved make an arithmetic progression? and why?
The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time.
Write first four terms of the A.P. when the first term a and the common differenced are given as follows:
a = -2, d = 0
Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.
10, 10 + 25, 10 + 26, 10 + 27,...
Find n if the given value of x is the nth term of the given A.P.
25, 50, 75, 100, ...; x = 1000
Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.
12, 32, 52, 72, ...
Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.
12, 52, 72, 73, ...
Find the common difference of the A.P. and write the next two terms \[0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, . . . \]
The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.
If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is
One person borrows ₹ 4,000 and agrees to repay with a total interest of ₹ 500 in 10 instalments. Each instalment being less than the preceding instalment by ₹ 10. What should be the first and the last instalments?
Common difference, d = ? for the given A.P., 7, 14, 21, 28 ........
Activity :- Here t1 = 7, t2 = 14, t3 = 21, t4 = `square`
t2 − t1 = `square`
t3 – t2 = 7
t4 – t3 = `square`
Therefore, common difference d = `square`
If (p + q)th term of an A.P. is m and (p - q)th term is n, then pth term is ______.
If the common difference of an AP is 3, then a20 - a15 is ______.
Verify that the following is an AP, and then write its next three terms.
`sqrt(3), 2sqrt(3), 3sqrt(3),...`
Which of the following form an AP? Justify your answer.
2, 22, 23, 24,...
How many terms are present in the sequence of A.P. 6, 11, 16, 21, ......... whose sum is 969?
The next term of the A.P. : `sqrt(6), sqrt(24), sqrt(54)` is ______.
