Advertisements
Advertisements
Question
Write the formula of the sum of first n terms for an A.P.
Advertisements
Solution
Sum of the first n terms is given by
`S_n = n/2[2a + (n - 1)d]`,
where a = first term,
d = common difference
OR
`S_n = n/2(t_1 + t_n)`,
where t1 = first term,
tn = last term
APPEARS IN
RELATED QUESTIONS
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.
If the mth term of an A.P. is 1/n and the nth term is 1/m, show that the sum of mn terms is (mn + 1)
Find the sum of first 40 positive integers divisible by 6.
In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64, find n.
Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………
If (2p – 1), 7, 3p are in AP, find the value of p.
The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.
The sum of first n terms of an A.P is 5n2 + 3n. If its mth term is 168, find the value of m. Also, find the 20th term of this A.P.
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is
If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is
The sum of first 14 terms of an A.P. is 1050 and its 14th term is 140. Find the 20th term.
What is the sum of an odd numbers between 1 to 50?
The sum of first ten natural number is ______.
Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
Find the middle term of the AP. 95, 86, 77, ........, – 247.
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.)
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
