Advertisements
Advertisements
Question
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
Options
0
5
6
15
Advertisements
Solution
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is 0.
Explanation:
Given,
a = –5
And d = 2
∴ S6 = `6/2[2a + (6 - 1)d]` ...`[∵ S_n = n/2[2a + (n - 1)d]]`
= 3[2(–5) + 5(2)]
= 3(–10 + 10)
= 0
APPEARS IN
RELATED QUESTIONS
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Find the sum of first 40 positive integers divisible by 6.
Find the sum of first 15 multiples of 8.
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
If Sn denote the sum of n terms of an A.P. with first term a and common difference dsuch that \[\frac{Sx}{Skx}\] is independent of x, then
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
The common difference of the A.P.
x is nth term of the given A.P. an = x find x .
An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installment is Rs. 100 less than the previous one, find:
- amount of installments paid in the 9th month.
- total amount paid in the installment scheme.
Q.14
Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.
The sum of all two digit odd numbers is ______.
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
