Question

Write the formula of sum an

a.p. when first term , last term and number of terms are given.also find 11th term of

a.p. 90, 80, 70, 60 ........

Answer 1

an={a(n-1)d}.........

Answer 2

Answer:

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

$T_{11}= -10$

Step-by-step explanation:

Given : Series of an A.P  90, 80, 70, 60 ........

To Write : The formula of sum $a_n$ when first term , last term and number of terms are given and also find 11th term of the given series

Solution :

Arithmetic progression sum is defined as

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

Where a is the first term, d is the common difference and n is the number of terms.

Now, The given series 90, 80, 70, 60 ........

Where first term a= 90,

common difference d= 80-90=70-80....= -10

To find the 11th term formula is $T_{n}=a+(n-1)d$

where n=11

$T_{11}=90+(11-1)(-10)$

$T_{11}=90+(10)(-10)$

$T_{11}=90-100$

$T_{11}= -10$

Therefore, The 11th term is -10.