# AP calculus

posted by .

The sixth term of an Arithmetic Progression is 23 and the sum of the six terms is 78. Find the first term and the common difference.

• AP calculus -

a+5d = 23
6/2 * [a + (a+5d)] = 78

a + 5d = 23
6a + 15d = 78

a=3
d=4

sequence: 3 7 11 15 19 23
sum: 78

• AP calculus -

Given an arithmetic progression -7,-3,1,..., state three consecutive terms in this progression which sum up to 75.

• AP calculus -

The kth term is a+(k-1)d
so you want

3a + (k-1 + k + k+1)d = 75

3(-7) + 3k(4) = 75
12k = 96
k=8

So, the 8th,9th,10th terms are

• AP calculus -

I can already tell that's gonna be super hlepufl.

## Similar Questions

1. ### arithmetic

an arithmetic progression has 20 terms. the sum of all the even terms is 350. given that the first term is 5, find the common difference and the eleventh term.
2. ### arithmetic

In an arithmetic progression the sum of the first 10 terms is 50 and the 5th is three times the second term. Find the fisrt term and the common difference.
3. ### maths

1) The first term of arithmetic progression is -20 and the sum of it's term is 250. find it's last term if the number of it's terms is 10 2) Find the fifth term from the arithmetic progression -12, -9, -6 hence find the sum of it's …
4. ### Maths

1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is …
5. ### Arithmetic Progressions

The second term of an arithmetic progression I four times the fits term, and the first term is ten. Find the common difference and hence find the sum of the first 12 terms.
6. ### Math

The fifth term of an arithmetic progression is 19 and the fourteenth term is 15. Find the, first term, common difference, and sum of the first eighty terms.
7. ### math

An arithmetic progression has 2 as its first term. find its common difference if the sum of 33 terms is equal to six times the sum of 13 terms
8. ### arithmetic

in an arithmetic progression the 13th term is 27 and the 7th term is three times the second term find;the common difference,the first term and the sum of the first ten terms
9. ### math C2 sequences and series

The eight,fourth and second terms of an arithmetic progression form the first three terms of a geometric series. The arithmetic progression has first term A and common difference d, and the geometric progression has first term G and …
10. ### Math

In an arithmetic progression, the 5th term is six times the 1st term and the sum of the first six terms is 99. Find the 1st term and the common difference. Attempt at solution: U5 = 6(U1) 99 = 3(2[U1] + 2d)

More Similar Questions