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Standard X

Mathematics

nth Term of an AP

A Find the su...

Question

(A) Find the sum of the following finite series

(a) 1 + 6 + 11 + 16 + ………+ 96

(b) 1 + 4 + 7 + ……..+ 73

(B) Find the number of terms in the following series if

(a) 3 + 5 + 7 + ……..= 624

(b) 15 + 12 + 9 + 6 + ……..−90

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Solution

(A) The sum of the first n terms of an A.P. is

(a)

The given series is an A. P. with and .

Thus, the given series has 20 terms.

The sum of the given series can be calculated as:

(b)

The given series is an A. P. with and .

Thus, the given series has 25 terms.

The sum of the given series can be calculated as:

(B)

(a) It is given that the sum of the series is 624.

The given series is an A. P. with and .

Also,

Thus, there are 24 terms in the given series.

(b) It is given that the sum of the series is −90.

The given series is an A. P. with and .

Also,

Thus, there are 15 terms in the given series.

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Similar questions

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

(v) $\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

(iii) $\frac{- 3}{4} \times (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Q. The sum of the following series

1 + 6 + \frac{9 (1^{2} + 2^{2} + 3^{2})}{7} + \frac{12 (1^{2} + 2^{2} + 3^{2} + 4^{2})}{9} + \frac{15 (1^{2} + 2^{2} + . . . . + 5^{2})}{11} + . . . . .

up to

15

terms is:

Q. The sum of the following series

1 + 6 + \frac{9 (1^{2} + 2^{2} + 3^{2})}{7} + \frac{12 (1^{2} + 2^{2} + 3^{2} + 4^{2})}{9} + \frac{15 (1^{2} + 2^{2} + . . . + 5^{2})}{11} + . . . up to 15 terms

, is :

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(A) Find the sum of the following finite series (a) 1 + 6 + 11 + 16 + ………+ 96 (b) 1 + 4 + 7 + ……..+ 73 (B) Find the number of terms in the following series if (a) 3 + 5 + 7 + ……..= 624 (b) 15 + 12 + 9 + 6 + ……..−90

(A) Find the sum of the following finite series

(a) 1 + 6 + 11 + 16 + ………+ 96

(b) 1 + 4 + 7 + ……..+ 73

(B) Find the number of terms in the following series if

(a) 3 + 5 + 7 + ……..= 624

(b) 15 + 12 + 9 + 6 + ……..−90