Question

Find the sum of first 35 terms of the series whose pth term is p/7 +2

Answer 1

Are you sure it is p ?

Answer 2

Ohh okay

Answer 3

\[\large{a_p = \cfrac{p}{7} + 2}\]

Answer 4

a+(p-1)d =.........

Answer 5

First you have to be sure that it is an AP

Answer 6

To check that calculate the difference between two consecutive terms

Answer 7

It is an AP , it is given under AP, but let us check anyway

Answer 8

\[\large{a_p - a_{p-1} = \cfrac{p}{7}-\cfrac{p-1}{7}}\]

\[\large{\implies a_p - a_{p-1} = \cfrac{p - p +1}{7} = \cfrac{1}{7}}\]

Now this is independent of p, thus it is an ap

Answer 9

why p/7 and p-1/7

Answer 10

i mean how

Answer 11

\(\color{blue}{\text{Originally Posted by}}\) @No.name
the series whose pth term is p/7 +2
\(\color{blue}{\text{End of Quote}}\)

If pth term was p/7 + 2, then (p-1)th term would have been (p-1)/7 + 2

I cancelled out the 2 as both a_p and a_(p-1) had "+2"

Answer 12

uhm yess

Answer 13

Good.

Now, if this is an ap, then the difference of the consecutive terms = common difference = d

Answer 14

yes..

Answer 15

I got it here, the sollution
http://yourmathguru.com/forums/topic/summation-4

Answer 16

the last sollution

Answer 17

That was the same as the one using \(\large{\sum}\)

Answer 18

Oh i have to go , will contuinue tommorow bye!

Answer 19

bye