Question

The sum of the 10th term and 16th term of an arithmetic sequence is 78. (a)Calculate its 13th term? (b)Find the sum of 5th term and 21st term​

Answer 1

Step-by-step explanation:

Let

′

a

′

and

′

d

′

arefirsttermand

Common \: difference \: of \:an \: A.PCommondifferenceofanA.P

\boxed{\pink{n^{th}\:term (a_{n}) = a+(n-1)d}}

n

th

term(a

n

)=a+(n−1)d

Sum \: of \: 10^{th} \:term \:and \:16^{th} \:termSumof10

th

termand16

th

term

= 78 \: (given)=78(given)

\implies a+9d + a + 15d = 78⟹a+9d+a+15d=78

\implies 2a + 24d = 78⟹2a+24d=78

/* Dividing each term by 2 , we get */

\implies a + 12d = 39⟹a+12d=39

\implies a + (13 - 1 )d = 39⟹a+(13−1)d=39

\implies a_{13} = 39⟹a

13

=39

Therefore.,

\red{ 13^{th} \:term \:in \: given \:A.P} \green{=39}13

th

termingivenA.P=39

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