Question

If the nth term of an ap is 7 - 3n find the sum of first 20 terms

Answer 1

First term = 7 - 3( 1 )
First term = 7 - 3
First term = 4


Second term = 7 - 3( 2 )
Second term = 7 - 6
Second term = 1





Common difference = second term - first term

Common difference = 1 - 4

Common difference is - 3





20th term = 7 - 3( 20 )
20th term = 7 - 60
20th term = -53







$\mathbf{we \: know \: \: s_{n} = \frac{n}{2} (a + l)}$


Hence,


$s_{20} = \frac{20}{2} (4 - 53) \\ \\ = > s_{20} = 10( - 49)$




Sum of first 20 terms is -490

Answer 2

Heya !!





Tn = 7 - 3n




T1 = 7 - 3 × 1 = 7 - 3 = 4




T2 = 7 - 3 × 2 = 7 - 6 = 1





T3 = 7 - 3 × 3 = 7 - 9 = -2










First term ( a ) = 4




Common difference ( d ) = t2-t1 = 1-4 = -3







We know that,



Sn = N/2 × [ 2A + ( n - 1 ) × D ]





S20 = 20/2 × [ 2 × 4 + ( 20 - 1 ) × -3 ]







=> 10 × ( 8 - 57 )




=> 10 × (-49)



=> -490.




Hence,



Sum of first 20 terms of the given ap will be equal to -490.