If the sum of first n terms of an AP is 1 2 ( 3 n 2 + 7 n ) , then find its n th term. Hence, write its 20 th term.

Let a be the first term and d be the common difference. It is given that sum of the first n terms of an A.P. is 1 2 ( 3 n 2 + 7 n ) . First term = a = S 1 = 1 2 [ 3 ( 1 ) 2 + 7 ( 1 ) ] = 5 Sum of first two terms = S 2 = 1 2 [ 2 ( 2 ) 2 + 7 ( 2 ) ] = 13 Second term = a 2 = S 2 - S 1 = 13 - 5 = 8 . Common difference = d = Second term - First term = 8 – 5 = 3 Also, n th term = a n = a + ( n - 1 ) d . ⇒ a n = 5 + ( n - 1 ) ( 3 ) ⇒ a n = 5 + 3 n - 3 ⇒ a n = 3 n + 2 Thus, n t h term of this A.P. is 3 n + 2 . Now, a 20 = a + ( 20 - 1 ) d ⇒ a 20 = 5 + 19 ( 3 ) ⇒ a 20 = 5 + 57 ⇒ a 20 = 5 + 57 Thus, 20 t h term of this A.P is 62 .

E M B I B E

CBSE Syllabus Standard Mathematics for Class X>Chapter 5 - Arithmetic Progressions>Execise 5.3>Q 21

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If $S_{n}$ , the sum of first $n$ terms of an AP is given by $S_{n} = 3 n^{2} - 4 n$ , find the $n^{th}$ term.

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Important Questions on Arithmetic Progressions

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CBSE Syllabus Standard Mathematics for Class X>Chapter 5 - Arithmetic Progressions>Execise 5.3>Q 21

If the sum of first

n

terms of an AP is

\frac{1}{2} (3 n^{2} + 7 n),

then find its

n^{th}

term. Hence, write its

20^{th}

term.

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CBSE Syllabus Standard Mathematics for Class X>Chapter 5 - Arithmetic Progressions>Execise 5.3>Q 22

In an AP, if the sum of its first

n

term is

3 n^{2} + 5 n

and its

k^{th}

term is

164

, find the value of

k

.

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CBSE Syllabus Standard Mathematics for Class X>Chapter 5 - Arithmetic Progressions>Execise 5.3>Q 22

The sum of first $q$ terms of an $A P$ is $63 q - 3 q^{2}$ . If its $p^{th}$ term is $- 60$ , find the value of $p$ . Also, find the $11^{th}$ term of its $A P$ .