Question

for an A.p find S7 and t20 if a= -5 and d=4
plzz solve this question step by step fast i will mark you as brainlist

Answer 1

According To question
a = (-5) , d = 4 then,
t20 = a + 19d
t20 = -5 + 19×4
t20 = -5 + 76
t20 = 71
And ,
S7 = 7÷2 [2×(-5) + (7-1)4]
= 7/2 [ -10 +24]
= 7/2 [ 14]
= 7×14 ÷ 2
= 7 × 7
= 49

Hope you like this answer. .............

Answer 2

Answer:

$\boxed{\red{\sf\:t_{20}\:=\:71}}\sf\:\:\:\&\:\:\:\boxed{\red{\sf\:S_7\:=\:49}}$

Step-by-step-explanation:

We have given the first term ( a ) and common difference ( d ).

We have to find the 20th term and the sum of first 7 terms.

$\bullet\sf\:a\:=\:-\:5\\\\\\\bullet\sf\:d\:=\:4$

We know that,

$\pink{\sf\:t_n\:=\:a\:+\:(\:n\:-\:1\:)\:d}\sf\:\:\:-\:-\:[\:Formula\:]\\\\\\\implies\sf\:t_{20}\:=\:-\:5\:+\:(\:20\:-\:1\:)\:\times\:4\\\\\\\implies\sf\:t_{20}\:=\:-\:5\:+\:19\:\times\:4\\\\\\\implies\sf\:t_{20}\:=\:-\:5\:+\:76\\\\\\\implies\boxed{\red{\sf\:t_{20}\:=\:71}}$

Now, we know that,

$\pink{\sf\:S_n\:=\:\dfrac{n}{2}\:\big[\:2a\:+\:(\:n\:-\:1\:)\:d\:\big]}\sf\:\:-\:-\:-\:[\:Formula\:]\\\\\\\implies\sf\:S_7\:=\:\dfrac{7}{2}\:\big[\:2\:\times\:(\:-\:5\:)\:+\:(\:7\:-\:1\:)\:\times\:4\:\big]\\\\\\\implies\sf\:S_7\:=\:\frac{7}{2}\:\big[\:-\:10\:+\:6\:\times\:4\:\big]\\\\\\\implies\sf\:S_7\:=\:\frac{7}{2}\:\big[\:-\:10\:+\:24\:\big]\\\\\\\implies\sf\:S_7\:=\:\frac{7}{\cancel2}\:\times\:\cancel{14}\\\\\\\implies\sf\:S_7\:=\:7\:\times\:7\\\\\\\implies\boxed{\red{\sf\:S_7\:=\:49}}$

Additional Information:

1. Arithmetic Progression:

1. In a sequence, if the common difference between two consecutive terms is constant, then the sequence is called as Arithmetic Progression ( AP ).

2. $\sf\:n^{th}$ term of an AP:

The number of a term in the given AP is called as $\sf\:n^{th}$ term of an AP.

3. Formula for $\sf\:n^{th}$ term of an AP:

$\large{\boxed{\red{\sf\:t_{n}\:=\:a\:+\:(\:n\:-\:1\:)\:d}}}$

4. The sum of the first n terms of an AP:

The addition of either all the terms of a particular terms is called as sum of first n terms of AP.

5. Formula for sum of the first n terms of A. P. :

$\large{\boxed{\red{\sf\:S_{n}\:=\:\frac{n}{2}\:\big[\:2a\:+\:(\:n\:-\:1\:)\:d\:\big]}}}$