Question

Find 26th and general term of the A.P., whose 6th term is 19 and 17th term is 41.

Answer 1

Answer:

59

Step-by-step explanation:

a+(n-1)d;

The 6th term is 19

a+5d=19-------(1)

The 17th term is 41

a+16d=41------(2)

By solving eqn(1) and (2)

a+5d=19

a+16d=41

We get

d=2,a=9

The 26th term is=a+25d

9+25(2)

9+50

59.....

Answer 2

GIVEN :

6th term of AP = 19

17th term of AP = 41

TO FIND:

26th and general term

FORMULA USED :

nth term of an AP (Tn) = a + (n-1)d

where =>

• a= first term
• n = number of term
• d = common difference

SOLUTION :

6th term can be written as =>

a +(6-1)d

a + 5d

but it is given that 6th term = 19

so , a + 5d = 19

Also , a= 19-5d

17th term can be written as =>

a +(17-1)d

a + 16d

dbut it is given that 17th term = 41

so , a + 16d = 41

Also , a= 41-16d

therefore,

19-5d = 41-16d

19-41=5d-16d

-22=-11d

22/11= d

2= d

a= 19-5d

= 19-10

= 9

so, a= 9 and d= 2

26th term = >

a+ (26-1)d

9+(25×2)

9+50

59

ANSWER :

General term = 9 + (n-1)2

26th term = 59

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