Let-T-k-is-the-k-th-term-and-S-k-is-the-sum-of-the-first-k-term-in-arithmetic-progression-If-T-3-T-6-T-9-T-12-T-15-T-18-45-Find-S-20-

Question Number 24677 by Joel578 last updated on 24/Nov/17

Let T_{k} is the k^{th} term and S_{k} is the sum

of the first k term in arithmetic progression

If T_{3} + T_{6} + T_{9} + T_{12} + T_{15} + T_{18} = 45

Find S_{20}

Answered by jota+ last updated on 24/Nov/17

6 T_{1} + (2 + 5 + 8 + 11 + 14 + 17) r = 45

2 T_{1} + 19 r = 15

T_{1} + (T_{1} + 19 r) = 15

T_{1} + T_{20} = 15

S_{20} = 15 \times 10

Commented by Joel578 last updated on 22/Dec/17

t h a n k y o u v e r y m u c h

Answered by ajfour last updated on 22/Dec/17

3 (T_{3} + T_{6} + T_{9} + \dots + T_{18}) = 135

\Rightarrow (T_{2} + T_{3} + T_{4}) + (T_{5} + T_{6} + T_{7}) + . .

\dots . + (T_{17} + T_{18} + T_{19}) = 135 . . (i)

a n d (\frac{T_{1} + T_{20}}{2}) \times 20 = S_{20}

\Rightarrow T_{1} + T_{20} = \frac{S_{20}}{10} \dots . (i i)

a d d i n g (i) a n d (i i)

S_{20} = 135 + \frac{S_{20}}{10}

\Rightarrow S_{20} = 135 \times \frac{10}{9} = 150 .

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