If-S-n-sum-of-sequence-2n-2-n-Find-the-value-of-the-1002-term-

Question Number 7656 by Tawakalitu. last updated on 07/Sep/16

I f S_{n} (s u m o f s e q u e n c e) = 2 n^{2} + n

F i n d t h e v a l u e o f t h e 1002 t e r m

Commented by prakash jain last updated on 12/Sep/16

n^{t h} term T_{n} = S_{n} - S_{n - 1}

= 2 n^{2} + n - 2 {(n - 1)}^{2} - (n - 1)

= 2 n^{2} + n - 2 n^{2} + 4 n - 2 - n + 1

= 4 n - 1

T_{1002} = 4 \times 1002 - 1 = 4007

Answered by Rasheed Soomro last updated on 09/Sep/16

S_{n} = 2 n^{2} + n

t_{1002} = ?

L e t a a n d d a r e f i r s t t e r m a n d c o m m o n d i f f e r e n c e

o f t h e A P .

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

L e t f i r s t d e t e r m i n e s u m o f 2003 t e r m s, w h i c h

w i l l h e l p u s t o d e t e r m i n e t_{1002} .

S_{2003} = \frac{2003}{2} [2 a + (2003 - 1) d] = 2 {(2003)}^{2} + 2003

= [2 a + 2002 d] = \frac{2 {(2003)}^{2} + 2003}{2003} \times 2

2 [a + 1001 d] = [2 (2003) + 1] \times 2

a + (1002 - 1) d = \frac{[2 (2003) + 1] \times 2}{2} = 4006 + 1 = 4007

t_{1002} = 4007

Commented by Tawakalitu. last updated on 09/Sep/16

T h a n k s b u t t h e y w r o t e 4007 h e r e a s a n s w e r . m a y b e t h e y a r e w r o n g

t h a n k s s i r .

Commented by Rasheed Soomro last updated on 09/Sep/16

T h e y a r e r i g h t . T h e r e w a s a m i s t a k e i n m y a n s w e r .

I h a d m u l t i p l i e d b y 2 i n s t e a d o f d i v i d e d i n l a s t t w o s t e p s .

I h a v e c o r r e c t e d i t n o w . S o r r y f o r m i s t a k e!

Commented by Tawakalitu. last updated on 11/Sep/16

T h a n k s s o m u c h . i r e a l l y a p p r e c i a t e .

Commented by Tawakalitu. last updated on 11/Sep/16

T h a n k s s o m u c h . i r e a l l y a p p r e c i a t e .