Question

12. Find the sum of n terms of an AP whose rth term is (5r+1).
13. If the sum of a certain number of terms of the AP 27, 24, 21, 18, ... is -30, find
the last term.​

Answer 1

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Answer 2

Question :- 12

• Find the sum of n terms of an AP whose rth term is (5r+1).

Solution :-

To Find:The sum of n terms of an AP.

Given:

The rth term of the series is given by

$t_r = 5r + 1$

Sum of the series is given by sum upto n terms of tr

$S_r = \frac{5n(n+1)}{2} +n$

Question :-13

• If the sum of a certain number of terms of the AP 27, 24, 21, 18, ... is -30, find the last term.

Solution :-

To Find: Last term of the AP.

Let the number of terms be n.

Sn = n/2 [2a + (n-1)d]

Sn = n/2 [ 54 + (n-1) ×(-3) ] = - 30

n [ 54 - 3n +3] = - 60

3n^2 - 57n - 60 =0

• ( Here we have to solve this quadratic equation )

Hence we got two values of n

Either n = 20 or n = - 1 ( n can not be negative)

Therefore n= 20

Also,

Sn = n/2 (n+l) [ Where l is last term ]

-30 = 20/2 ( 20 + l )

-30 = 270 + 10l

l = - 30

Hence,

The last term is = - 30