To find the sum of a number of terms in Arithmetical Progression:
Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..
Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..To find the sum of n terms of a GP
Let a = First term, r = common ratio, n = number of terms. Multiply both sides of (i) by r, the common ratio. Subtracting (ii) from (i), we get ..
Let a = First term, r = common ratio, n = number of terms. Multiply both sides of (i) by r, the common ratio. Subtracting (ii) from (i), we get ..Harmonic Mean (H.M.)
Harmonic Mean (H.M.) - If three quantities are in harmonic progression, then the middle quantity is called the harmonic mean between the other two. Example: 1/3, 1/7, 1/11 are in H.P., then 1/7 is the middle term. Hence 1/7 is the harmonic..
Harmonic Mean (H.M.)
If three quantities are in harmonic progression, then the middle quantity is called the harmonic mean between the other two. Example: 1/3, 1/7, 1/11 are in H.P., then 1/7 is the middle term. Hence 1/7 is the harmonic mean between 1/3 and 1/1..
The sum of n terms of an Arithmetic Progression, Sn, is given by the f..
The sum of n terms of an Arithmetic Progression, S n , is given by the formula S n = n 2 ( a + l ) , where a is the first term and l is the last term of the A.P. Find the first term of the A.P if its..
In an arithmetic series whose first term is 168, nth term is - 8 with ..
In an arithmetic series whose first term is 168, n th term is - 8 with common difference as - 4. Find the sum of first n terms of the series. => 3610 or 3590 or 7200 or 3600..
Sum to n terms of a geometric series is (9n - 1). Find the 10th term.
Sum to n terms of a geometric series is (9 n - 1). Find the 10 th term. => 8(9 9 ) or 9 10 - 1 or 9 1 0 9 9 or 9(9 9 )..
Sum to n terms of a geometric series is (5n - 1). Find the 43th term.
Sum to n terms of a geometric series is (5 n - 1). Find the 43 th term. => 5(5 42 ) or 5 4 3 5 4 2 or 4(5 42 ) or 5 43 - 1..
Find the sum of n terms of the geometric series 1 + 6 + 36 + 216 + ....
Find the sum of n terms of the geometric series 1 + 6 + 36 + 216 + ... . => 1 5 (6 n - 1) or 1 6 (6 n + 1) or 6(6 n - 1) or (6 n + 1)..
Find the sum to n terms of the geometric series.1 + 10 + 100 + 1000 +..
Find the sum to n terms of the geometric series. 1 + 10 + 100 + 1000 + ... => 1 9 (1 - 10 n ) or n 2 [ 2 + ( n - 1 ) 9 ] or 10 n - 1 or 1 9 (10 n - 1)..
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