Gyaan School

Login

Register Now

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Morbi adipiscing gravdio, sit amet suscipit risus ultrices eu. Fusce viverra neque at purus laoreet consequa. Vivamus vulputate posuere nisl quis consequat.

Register Now

Lost Password

Lost your password? Please enter your username and email address. You will receive a link to create a new password via email.

Home / Problem Set 3

In an A.P. the first term is –5 and last term is 45. If sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?

Print or Save

Sol. For the given A. P.
First term a = –5

t_n = 45
S_n = 120
∴ t_n = a + (n –1)d
45 = –5 + (n –1)d
45 + 5 = (n –1)d
(n –1)d = 50 ...(I)

S_n = \({n\over2}[2a+(n-1)d]\) [Formula]

120 = \({n\over2}[2*(-5)+50]\) [From (I)]

240 = n [ –10 + 50]
240 = n × 40
n = 6
Place n = 6 in eqn. (I)
(6 – 1)d = 50

d = \(50\over 5\)

d = 10

∴ There are 6 terms in the A. P. and the common difference is 10.

Arithmetic Progression September 28 , 2018 0 Comments 407 views

Login

Register Now

Register Now

Lost Password

In an A.P. the first term is –5 and last term is 45. If sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?

Print Document

Related questions

₹1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. Arithmetic Progression

If m times the mth term of an A.P. is equal to n times nth term then show that the (m + n)th term of the A.P. is zero. Arithmetic Progression

If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q) Arithmetic Progression

If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is \({(a-c)(b+c-2a)}\over 2(b-a)\) Arithmetic Progression

There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P. Arithmetic Progression

₹1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years.

Arithmetic Progression

If m times the m^th term of an A.P. is equal to n times n^th term then show that the (m + n)^th term of the A.P. is zero.

Arithmetic Progression

If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)

Arithmetic Progression

If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is \({(a-c)(b+c-2a)}\over 2(b-a)\)

Arithmetic Progression

There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.

Arithmetic Progression