Question

Determine the first term and the 40th term of an AP whose 7th term is 34 and 15th term is 74.

Answer 1

Step-by-step explanation:

Tn= a+(n-1)d

34= a+(7-1)d

34= a+6d

34-6d=a

again

Tn=a+(n-1)d

74= a+(15-1)d

74= a+14d

putting a=34-6d in equation,

74= 34-6d+14d

40= 8d

5= d

34-6d= a

34-(6×5)=a

34-30=a

4=a

tn= a+(n-1)d

= 4+(40-1)5

= 4+39×5

= 4+195

= 299

hence first term be 4 and 40th term be 299

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