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

Question

vishweshshrimali5 · Answer

Are you sure it is p ?

vishweshshrimali5 · Answer

Ohh okay

vishweshshrimali5 · Answer

$$\large{a_p = \cfrac{p}{7} + 2}$$

anonymous · Answer

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

vishweshshrimali5 · Answer

First you have to be sure that it is an AP

vishweshshrimali5 · Answer

To check that calculate the difference between two consecutive terms

anonymous · Answer

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

vishweshshrimali5 · Answer

$$\large{a_p - a_{p-1} = \cfrac{p}{7}-\cfrac{p-1}{7}}$$

$$\large{\implies a_p - a_{p-1} = \cfrac{p - p +1}{7} = \cfrac{1}{7}}$$

Now this is independent of p, thus it is an ap

anonymous · Answer

why p/7 and p-1/7

anonymous · Answer

i mean how

vishweshshrimali5 · Answer

$\color{blue}{\text{Originally Posted by}}$ @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"

anonymous · Answer

uhm yess

vishweshshrimali5 · Answer

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

anonymous · Answer

yes..

anonymous · Answer

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

anonymous · Answer

the last sollution

vishweshshrimali5 · Answer

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

anonymous · Answer

Oh i have to go , will contuinue tommorow bye!

vishweshshrimali5 · Answer

bye