How i solve the question of arithmetic progressions of ncert of class 10th How i solve the class 10th question of exercise 5.2 Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.

AnilSinghBoraGuru

# Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P. Q.1

Share

(i)Given,First term,

a= 7Common difference,

d= 3Number of terms,

n= 8,We have to find the nth term,

a= ?_{n}As we know, for an A.P.,

a=_{n}a+(n−1)dPutting the values,

=> 7+(8 −1) 3

=> 7+(7) 3

=> 7+21 = 28

Hence,

a= 28_{n}(ii)Given,First term,

a= -18Common difference,

d= ?Number of terms,

n= 10Nth term,

a= 0_{n}As we know, for an A.P.,

a=_{n}a+(n−1)dPutting the values,

0 = − 18 +(10−1)

d18 = 9

dd= 18/9 = 2Hence, common difference,

d= 2(iii)Given,First term,

a= ?Common difference,

d= -3Number of terms,

n= 18Nth term,

a= -5_{n}As we know, for an A.P.,

a=_{n}a+(n−1)dPutting the values,

−5 =

a+(18−1) (−3)−5 =

a+(17) (−3)−5 =

a−51a= 51−5 = 46Hence,

a= 46(iv)Given,First term,

a= -18.9Common difference,

d= 2.5Number of terms,

n= ?Nth term,

a= 3.6_{n}As we know, for an A.P.,

a=_{n}a+(n−1)dPutting the values,

3.6 = − 18.9+(

n−1)2.53.6 + 18.9 = (

n−1)2.522.5 = (

n−1)2.5(

n– 1) = 22.5/2.5n– 1 = 9n= 10Hence,

n= 10(v)Given,First term,

a= 3.5Common difference,

d= 0Number of terms,

n= 105Nth term,

a= ?_{n}As we know, for an A.P.,

a=_{n}a+(n−1)dPutting the values,

a= 3.5+(105−1) 0_{n}a= 3.5+104×0_{n}a= 3.5_{n}Hence,

a= 3.5_{n}