Question

fifth term of an arithmetic sequence is 10 and 10th term is 5
what is common difference
what is first term
what is fifteenth term
what is the sum of product of fifteen terms​

Answer 1

$\huge\tt\underline\blue{Question}$

-fifth term of an arithmetic sequence is 10 and 10th term is 5

-what is common difference

-what is first term

-what is fifteenth term

-what is the sum of product of fifteen terms

$\huge\tt\underline\red{❥︎ Answer࿐}$

$\huge\tt\underline\purple{given}$

a+4d=10

a+9d=5

$\huge\tt\underline\orange{to - find}$

common difference ¿

$\huge\tt\underline\pink{solution}$

solve equation (1) and (2)

a+4d=10

a+9d=5

- - -

-5d=5

d= -1

$\huge\tt\underline\blue{common -difference- is : -1}$

second question

-what is first term

$\huge\tt\underline\pink{solution}$

put value of d in equation( 1)

a+4d=10

a+4(-1)=10

a-4=10

a=10+4

a=14

$\huge\tt\underline\pink{first- term- of -ap- is +14}$

third question

-what is fifteenth term

$\huge\tt\underline\green{solution}$

as we know, a= 14

and d = -1

so a15=a+(n-1)d

=14+(15-1)-1.

=14+14*(-1)

=14-14

=o

$\huge\tt\underline\red{fifteen -term -is - 0}$

fourth question

what is the sum of product of fifteen terms

product of 15 term will be zero because 15th term is 0

so their sum will be zero

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

or sum of 15 terms

sn=n/2 (2a+(n-1)d

=15/2(2*14-14)

=15/2(28-14)

=15/2(14)

=15*7

=105

$\huge\tt\underline\red{thanks}$

hope its helpful