The Fifth terms Of An A.P. Is 1 Whereas Its 31st Term Is – 77. Find Its 20th Term And Sum Of Its First Fifteen Terms. Also Find Which Term Of The Series Will Be  –17 And Sum Of How Many Terms Will Be 20.

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Question

The fifth terms of an A.P. is 1 whereas its 31st term is – 77. Find its 20th term and sum of its first fifteen terms. Also find which term of the series will be  –17 and sum of how many terms will be 20.

Solution

Correct option is

n = 8

        .  

Solving the above two, we get 

            a = 13 and d = –3.                … (i)   

         

              

Let    Tn = –17. Then a + (n – 1)d = –17      

        

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The value of n cannot be fractional.

Testing

SIMILAR QUESTIONS

Q1

The nth term of a series is given to be , find the sum of 105 terms of this series. 

Q2

Find the sum of the first 24 terms of the A.P. a1a2a3, … If it is known that .

Q3

…to n terms.

Q4

The third term of a G.P. is 4. The product of first five terms is

 

Q5

The A.M. between m and n the G.M. between a and b are each equal to (ma + nb)/(m + n). Find m and n in terms of a and b.

Q6

A.M. and H.M. between two quantities are 27 and 12 respectively, find their G.M.

Q7

The sum of three numbers in H.P. is 26 and sum of their reciprocals is 3/8. Find the numbers.

Q8

The harmonic mean of two numbers is 4, their A.M. A, and G.M. G, satisfy the relation 2A + G2 = 27. Find the two numbers.

Q9

If xyz are in G.P.,