Find the sum to n terms of the A.P., whose k th term is 5 k + 1.
The k t h term of A.P. is 5 k + 1 .
Let a , d be the first term and common difference of the given A.P.
The formula to find the terms in an A.P. is given by,
T n = a + ( n − 1 ) d
Substitute the values in the above expression.
T k = a + ( k − 1 ) × d 5 k + 1 = a + k d − d 5 k + 1 = k d + ( a − d )
Compare the coefficients on both the sides.
a − d = 1 d = 5
Solve the above expression to obtain the values of a and d .
d = 5 a = 6
The formula for the sum of n terms in A.P. is given by,
S n = n 2 [ 2 a + ( n − 1 ) d ]
Substitute the values of a and d , as 6 and 5 in the above expression.
S n = n 2 [ 2 × 6 + ( n − 1 ) × 5 ] S n = n 2 ( 12 + 5 n − 5 ) = n 2 ( 5 n + 7 )
Thus, the sum of n terms of A.P. is = n 2 ( 5 n + 7 ) .
The
Let
The formula to find the terms in an A.P. is given by,
Substitute the values in the above expression.
Compare the coefficients on both the sides.
Solve the above expression to obtain the values of
The formula for the sum of
Substitute the values of
Thus, the sum of
