In an A. P the term is -10 and the 15th term is 11 and the last term is 41. Find the sum of all terms in this progression.​

This is equivalent to the fraction 1085/2

Explanation:

AP stands for "arithmetic progression", which is another name for "arithmetic sequence"

a1 = -10 is the first term

the 15th term happens when n = 15, so

an = a1 + d*(n-1)

a15 = -10 + d(15-1)

a15 = 14d-10

Set this equal to 11 (the stated 15th term) and solve for d

a15 = 11

14d-10 = 11

14d = 11+10

14d = 21

d = 21/14

d = 3/2

d = 1.5 is the common difference

Let's find the nth term

an = a1 + d(n-1)

an = -10 + 1.5(n-1)

an = -10 + 1.5n - 1.5

an = 1.5n - 11.5

The last term is 41, so we'll replace the 'an' with that and solve for n

an = 1.5n - 11.5

41 = 1.5n - 11.5

41+11.5 = 1.5n

52.5 = 1.5n

1.5n = 52.5

n = (52.5)/(1.5)

n = 35

So the 35th term is 41.

We're summing n = 35 terms from a1 = -10 to an = 41

S = sum of the first n terms of arithmetic progression

S = (n/2)*(a1 + an)

S = (35/2)*(-10+41)

S = 542.5

The 35 terms add up to 542.5 which is the final answer

As an improper fraction, this converts to 1085/2

lo.lll

step-by-step explanation:

black/brown

step-by-step explanation:

well, you see here, jamal was born to 2 parents, his mother who he lives with and his father who left at a young age and who happens to be younger than him. he stole cookies because he has to steal food due to the fact that he spends his government poverty checks on pot and women.