Find the sums given below :

(i)

(ii)

(iii)

(i) Here, a = 7, d = 3.5 and last term = 84

Number of terms can be calculated as follows;

a_n =a + (n-1)d

Or, 84 = 7 + (n-1)3.5

Or, (n-1)3.5 = 84-7

Or, n - 1 = 77/3.5 = 22

Or, n = 23

Sum of n terms can be given as follows:

S₂₃

= (14 + 77)

=

=1046

(ii) Here, a = 34, d = - 2 and last term = 10

Number of terms can be calculated as follows:

an = a + (n – 1)d

Or, 10 = 34 + (n – 1)(- 2)

Or, 10 = 34 – (n – 1)(2)

Or, (n – 1)2 = 34 – 10 = 24

Or, n – 1 = 12

Or, n = 13

Sum of n terms can be given as follows:

S₁₃

= [+ ]

=

=

Thus, sum of the given AP (S_n)=

(iii) Here, a = - 5, d = - 3 and last term = - 230

Number of terms can be calculated as follows:

a_n = a + (n – 1)d

Or, - 230 = - 5 + (n – 1)( - 3)

Or, - 230 = - 5 – (n – 1)3

Or, (n – 1)3 = - 5 + 230 = 225

Or, n – 1 = 75

Or, n = 76

Sum of n terms can be given as follows:

S₂₃

= (-10 -225)

=

=-8930