Question

The 5th and 15th terms of an AP are 13 and -17 respectively. Find the sum of first 21 terms of the AP

Answer 1

Answer:

We know that in an AP, nth term, An = A + (n-1)d,

where An = nth term

A = first term of the AP

n = number of terms used

d= difference between two consecutive terms of AP

Also,  Sn =[n/2] [2 a + (n-1)d]

where, Sn = sum of n terms of AP.

Step-by-step explanation:

Now, A 5 = A + (5-1) d

13 = A + 4 d.......................equation 1

Similarly,  -17 = A + 14 d...............equation 2

On subtracting, equation 2 from equation 1,

we get, 30 = -10 d

or d = -3

and using d= -3 in equation 1, we get , 13 = A + 4(-3)

or, A=25

Now, S 21 = [21/2] [ 2 * 25 + (21-1) (-3)]

S 21 = [21/2] [50 + 20 * (-3) ]

S 21  = [21/2] [ 50 -60]

S 21 = [21/2] [-10]

S 21 = -210/2

S 21 = -105

Therefore, sum of first 21 terms of the AP IS -105.

Note- Do not confuse if the sum comes out to be negative. A negative answer means that the value of the negative terms in the AP is greater than the value of the positive terms of the AP.

Answer 2

Answer:

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