Question

The 5th and 15 term of an ap are 13 and -17 respectively find the sum of first 21 terms of the AP

Answer 1

a5=13

a+(n-1)d=a5
a+(5-1)d=13
a+4d=13 ----(1)

a15= -17
a+(n-1)d=a15
a+(15-1)d= -17
a+14d= -17 ---(2)

Solving eq. 1 and 2 we get

a+4d=13
a+14d=-17
---------------
-10d=30
d= -3

Putting the value of d in eq(1)
a+4×(-3)=13
a-12=13
a=13+12
a=25

Now we have to find the sum of first 21 terms:
Sn=n/2{2a+(n-1)d}
S21=21/2{2×25+(21-1)(-3)}
S21=21/2{50+20×(-3)}
S21=21/2(50-60)
S21=21/2×(-10)
S21= -210/2
S21= -105

Answer 2

Step-by-step explanation:

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